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## That the Ancient Sumerian Geometers 3 to 1 ratio, of a circles circumferential length to its diameter length, was and is correct.

Reference; “Will science ever tell us everything there is to know?”

During this conversation I was challenged to open a forum regarding my assertion, that a circle is 3 x its diameter length, and told its simple arithmetic would be devastated by the world’s geometers.

However let me make it clear, I am not interested in decimal approximates related to Pi; as hundreds of millions having learned simple arithmetic would agree, the arithmetic provided is correct.

Therefore the onus is upon others to prove that the simple arithmetic involved, is incorrect; and if not, the methodology is then proven.

Starting from a square measuring 120 by 120cm; the square has an area of 14, 400 sq cm & perimeter of 480cm

Taking one 120cm side of the square, we use it as a diameter and multiply by 3

Giving 360cm to the 360 degree circumferential length of the circle; which is ¾ quarters the length of its squares 480cm perimeter; and each degree of the circle is 1cm in length

So it follows as the circle is ¾ of the length of its squares perimeter; its area will also be ¾ that of its squares, 14,400 sq cm area.

Four methods for calculating the square area of a circle

1. 14,400 sq cm ÷ by 4 = 3,600 sq cm x 3 = 10,800 sq cm to the area of the circle

2. 120cm diameter ÷ by 2 = a radius of 60cm, squared = an area of 3,600 sq cm x 3 = 10, 800 sq cm to the area of the circle

Therefore the formula for finding the rational (equal divisibility) length, to the symmetry of a circle is; 3 times the circles diameter; and formula for area is r2 x 3

3. The 60cm radius squared gives an area of 3, 600 sq cm ÷ by 4 = 900 sq cm x 3 = 2, 700 sq cm x 4 = 10, 800 sq cm to the area of the circle

4. Sumerian Method: The circumference of the circle measures 360cm which is squared, giving an area of 129, 600 sq cm ÷ by 12 = 10, 800 sq cm to the area of the circle.

Note the latter method used by the Sumerian originators of geometry, was devised at least 1, 300 years before Archimedes was born.

• #### Evan S

• +1
Feb 28 2014: You're on the right track but a bit off on the ratio. It should be a 2 to 1 ratio of a circles circumferential length to its diameter length.

Starting from a square measuring 120 by 120cm; the square has an area of 14, 400 sq cm & perimeter of 480cm

Taking one 120cm side of the square, we use it as a diameter and multiply by 2

Giving 240cm to the 360 degree circumferential length of the circle; which is 1/2 the length of its squares 480cm perimeter; and each degree of the circle is 2/3cm in length

So it follows as the circle is 1/2 of the length of its squares perimeter; its area will also be 1/2 that of its squares, 14,400 sq cm area.

Four methods for calculating the square area of a circle

1. 14,400 sq cm ÷ by 4 = 3,600 sq cm x 2 = 7,200 sq cm to the area of the circle

2. 120cm diameter ÷ by 2 = a radius of 60cm, squared = an area of 3,600 sq cm x 2 = 7,200 sq cm to the area of the circle

Therefore the formula for finding the rational (equal divisibility) length, to the symmetry of a circle is; 2 times the circles diameter; and formula for area is r2 x 2

3. The 60cm radius squared gives an area of 3, 600 sq cm ÷ by 4 = 900 sq cm x 2 = 1,800 sq cm x 4 = 7,200 sq cm to the area of the circle

4. Sumerian Method: The circumference of the circle measures 240cm which is squared, giving an area of 57,600 sq cm ÷ by 8 = 7,200 sq cm to the area of the circle.

I checked it a few times and the arithmetic is correct.
• #### Raymond Cavallaro

• 0
Mar 20 2014: Carl Dalton,

Complementing Evan S answer, it can be done with any number, the math is right, the concept is not

Taking one 120cm side of the square, we use it as a diameter and multiply by 3

Where this 3 came from??

So it follows as the circle is ¾ of the length of its squares perimeter; its area will also be ¾ that of its squares, 14,400 sq cm area.

Where this 3/4 of the area came from?? (been 3/4 of perimeter doesnt mean that it will be 3/4 of area also)

Those are the points where you were wrong

Your answer could be easylly proven wrong empirically, make the circle you sugest and mesure it

both your answer would be correct if divide by 3 and multiply by pi

So the perimeter shall be ~377 instead of 360, you can see 17cm left when measuring
The area shall be ~11310 instead of 10800, you can measure throught a cilinder volume, filling with water
The cilinder would have volume of the circle area multiplied for the cilinder height
So with 1cm of height the cilinder volume shall be ~11310 instead of 10800 cm cubic of water
• #### Carl Dalton

• 0
Mar 20 2014: I suggest you refer to the post made by John Mauren on the first of march which ended with quote

"Consider your simple black and white arithmetic disproved and negated"

My response was to immediately then reply with the post "A square to its sphere" which gave the exact mathematical proportions; subject to empirical testing by weight, and using Archimedes principle volumes.

Result within a very short time; and I admire his honesty and would say thank you: he posted a thumbs up.

I then followed up with "Pi in Black and Yellow; defining the irrefutable logic relative to the symmetry of the area of a circle; relative to equalities of area to a circle relative to the equality of the area to its square.

The point being; I could not post these prior to first having explained the 3 - 1 ratio of the circle; however on posting both "A Cube to its Sphere" and :Pi in Black and Yellow.

The result being as I expected given that both are irrefutable proof, as to the 3-1 ratio; the conversation went silent/dead;

As generally speaking, people simply do not possess either the honesty or the courage, to simply say; sorry I got it wrong.

And I have little doubt that even when or if you do choose to read "A Cube to its Sphere" and "Pi in Black & Yellow.

Neither will you

However given that I have 8, 500 + followers of my web page, in 118 countries of 195, and 227, 000 + hits; and 2000+ years of precedence.

I have the strongest copyright relative to my intellectual property, on Earth; and regardless of those who refuse to believe it; the the truth as to the exact 3 - 1 ratio of a circle will grow and eventually have to be accepted.
• #### Raymond Cavallaro

• 0
Mar 20 2014: i didnt see you refutating my logic, where am i wrong in my argument?

did you draw a simple circle with a compass and measure with a simple string?

did you get 360 or 377 cm?
• #### John Mauren

• +1
Feb 28 2014: Forgive me if I'm mistaken... but challenging maths status quo along with 30+ comments to follow and not one mention of Sexagesimal numbering system?

From base-10 to 12, 24, 36, 48, 60 and even the rare 20.... it is not possible formulate a simple ratio such as 1:3 in attempts of squaring a circle to support the maxims you're proposing.

The following two books are great reads and will help explain the faults in your claims:

The Dynamics of Progress: Time, Method, and Measure
By Samuel L. Macey

The Linguistic Theory of Numerals
James R. Hurford

Also, I suggest subscribing to "Numberphile" on Youtube, as this topic and others surrounding it are covered in great length.
• #### Carl Dalton

• 0
Mar 1 2014: I will stick with the simple black and white arithmetic, which has not been disproved and cannot be negated, and four different methods, obtaining exactly the same result, serve to confirm it. And they are supported by my post yesterday re Euclidean and Sumerian geometry.

And it is not about squaring a circle, rather obtaining the area of a circle in the form of square area.
• #### John Mauren

• +1
Mar 1 2014: "The number π is a mathematical constant that is the ratio of a circle's circumference to its diameter and is approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes spelled out as "pi" (/paɪ/).

Being an irrational number, π cannot be expressed exactly as a common fraction. Consequently, its decimal representation never ends and never settles into a permanent repeating pattern. The digits appear to be randomly distributed, although no proof of this has yet been discovered. Also, π is a transcendental number – a number that is not the root of any nonzero polynomial having rational coefficients. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straight-edge."

http://en.wikipedia.org/wiki/Pi

One more time:

" the ratio of a circle's circumference to its diameter"

The title of this conversation that you started is:
"That the Ancient Sumerian Geometers 3 to 1 ratio, of a circles circumferential length to its diameter length, was and is correct."

Why is Sexagesima relevant?

"Sexagesimal (base 60) is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, it was passed down to the ancient Babylonians, and it is still used — in a modified form — for measuring time, angles, and geographic coordinates."
http://en.wikipedia.org/wiki/Sexagesimal

Geometry is geometry and your interpretation of the fundamental principals behind your calculations are incorrect in just about every notational manner relevant to the underlying context put forth.

Try using the following...

http://baptiste.meles.free.fr/site/mesocalc.html
(MesoCalc is a Mesopotamian calculator. It computes with integers in sexagesimal place-value notation and operates on measures.)

Consider your simple black and white arithmetic disproved and negated.
• #### Carl Dalton

• +1
Mar 1 2014: 1 more time "Fractions"

A Cube to its Sphere

Beginning from a wood cube measuring 6 x 6 x 6 centimeters, we have to imagine that we are turning it on a wood lathe, to produce a cylinder by removing 4 sides & ¼ of its mass. The cylinder is then replaced lengthwise, to remove the two circular faces, & ¼ of its mass to create the sphere.

12 steps to the Sphere

1. Measure the Cubes height to find the length of Diameter = 6 cm

2. Multiply the Diameter by itself, to obtain the Squares length and Square Area, = 24 cm and 36 sq cm

3. Multiply the Square Area by the diameter to obtain the Cubes Cubic Capacity = 216 cubic cm

4. Divide the Cubes Cubic Capacity by 4 to obtain ¼ of the Cubes Cubic Capacity = 54 cubic cm

5. Multiply the ¼ Cubic Capacity by 3 to obtain the ¾ Cubic Capacity of the Cylinder = 162 cubic cm

6. Multiply the Area of one Face of the Cube by 6 to obtain the Cubes Surface Area = 216 sq cm

7. Divide the Cubes Surface Area by 4 to obtain ¼ of the Cubes Surface Area = 54 sq cm

8. Multiply the ¼ Surface Area by 3 to obtain the ¾ Surface Area of the Cylinder = 162 sq cm

Cylinder to its Sphere

9. Divide the Cylinders Cubic Capacity by 4 to obtain ¼ of the Cubic Capacity = 40 ½ cubic cm

10. Multiply the ¼ Cubic capacity by 3 to obtain the ¾ Cubic Capacity of the Sphere = 121 ½ cubic cm

11. Divide the Cylinders Surface Area by 4 to obtain ¼ of the Surface Area = 40 ½ sq cm

12. Multiply the ¼ Surface Area by 3 to obtain the ¾ Surface Area of the Sphere = 121 ½ sq cm

Confirmation by weight using a "16 x 16 x 16 cm cube" weighing 160 grams

Given that a 16 x 16 x 16 Cube weighs 160 grams, prior to being turned on a wood lathe to remove 1/4
of its mass

A. The Cylinder will weigh 120 grams
B. The wood shavings will weigh 40 grams

Given the Cylinder weighs 120 grams prior to being turned on the wood lathe to remove 1/4 of its mass

A. The Sphere will weigh 90 grams
B. The wood shavings will weigh 30 grams

Archimedes Principle for volumes
• #### Raymond Cavallaro

• 0
Mar 20 2014: Carl Dalton,

A. The Cylinder will weigh 120 grams
B. The wood shavings will weigh 40 grams

you are wrong
i did it and i measure it, and the result was:

A. The Cylinder will weigh ~ 126 grams
B. The wood shavings will weigh ~ 34 grams

That is the exact values i said before, to take your answer divide for 3 and multiply for Pi

• +1
Feb 22 2014: "Giving 360cm to the 360 degree circumferential length of the circle; which is ¾ quarters the length of its squares 480cm perimeter; and each degree of the circle is 1cm in length"

Its pretty difficult to read math in the pre-Newton style (as paragraphs as opposed to equations), but I've tried, and I believe this is where your mistake lies.
You assume a square of that perimeter will encompass a circle of that perimeter, and go from there. The base assumption is incorrect.

As far as I'm aware, Pi was originally measured and proven empirically, but more modern mathematics actually have a proof for it. It does require some infinitesimal calculus though, so I won't get into it in detail.
The general gist of it involves starting with 1=y^2+x^2 to describe a two dimensional circle with a radius of 1 and a center at (0,0), and using calculus tools to figure out its arc length.
• #### Carl Dalton

• 0
Feb 23 2014: Quote: Its pretty difficult to read math in the pre-Newton style (as paragraphs as opposed to equations),

Rhetorical question:

If you find it difficult or cant read simple math presented in paragraphs, then how can you be sure you understand what I am talking about? Because from my perspective, you certainly can;t and I am not being nor do I wish to be, impolite or insulting in regard to this remark; I am thinking more in terms of a generation gap.

As to Newton great respect for the man, however;

Newtons first law states that an object will continue forward in a direct straight line, unless an external force acts upon it.

Reality: The centre of gravity of an object (Snooker Ball) will move directly forward in line with/from the point of impact, and cease when the energy of its impetus runs down.

A direct straight forward linear motion of an object can only be achieved. if a constant external force is applied to maintain its straight motion; e.g. a rolling ball needs a flat surface; a projectile will curve with gravity, unless aerodynamics or other external forces are applied.

You cannot walk in a straight line over the Earth's surface because it is curved, a straight line cannot be drawn, without pencil pressure (force) being applied, and a ruler to guide it, etc.

Cheers Carl
• #### Carl Dalton

• 0
Mar 22 2014: Summary of the five methods that can be used, for finding the area to a circle, using the 3 to 1 ratio of the circle to its diameter length; using a 120 x 120 cm square with an area of 14, 400 square cm, and a perimeter length of 480 cm,
Simplest first.

1. Using the 60 cm radius (1/2 right angle) multiply by 180 degrees = 10, 800 square cm to the circle.

2. Multiply the 60 cm radius by itself = 3, 600 square cm, and multiply by 3 = 10, 800 square cm to the circle.

3. Divide the 14, 400 square area of the square by 4, = 3, 600 square cm, and multiply by 3 = 10, 800 square cm to the circle.

4. Divide the area of the squared radius = 3, 600 square cm by 4 = 900 square cm; multiply by 3 = 2, 700 square cm; multiply by 4 = 10, 800 square cm to the circle.

5. Sumerian: Multiply the 120 cm diameter by 3 = 360 cm, and multiply this by itself; 360 x 360 = 129, 600 and divide by 12 = 10, 800 square cm to the circle.

Five methods/proofs and all results concur, because the 3 -1 ratio of a circle to its diameter length is exactitude, whereas Pi is simply an approximation of this exactitude.

For subsequent proofs based on this exactitude, refer to

From a Cube to its Sphere
Pi in Black & Yellow
Areas and volumes of symmetrical ovals and ovoids
Calculating the area of a ring

In conclusion

Five methods for finding the area to a circle and all five results concur; plus the subsequent building of a perfectly symmetrical sphere, based on the 3 to 1 ratio of the circle.

And only one person and major detractor subsequent to my providing this proof, had the common decency, honesty and courage to admit that my method was correct.

So what does this say of the human condition?

I will leave this consideration for the reader to determine, as I am now done with this conversation.
• #### Carl Dalton

• 0
Mar 21 2014: Further Clarification 21st March, Continued

Given that there is 14, 400 square cm to the area of the square; one quadrant of the square will have an area of 3, 600 square cm.

Given that there is 10, 800 square cm to the area of the circle; one quadrant of the circle will have an area of 2, 700 square cm.

Therefore it follows, that the remaining four areas, of the four arcs of outer quadrant (corners) to the square;

Have a square area of 900 square cm each, and when added together/combined, have a total area of 3, 600 square cm;

Which equates to the square area of one quadrant of the original square, which when added/combined with the 10, 800 square cm of the circle;

Equates to the 14, 400 square cm to the original square.

Has anyone who didn’t get it, got it now? Exempting Raymond Cavarello, who will never get it.

And note that was a rhetorical question; as very very few have the honesty, or the courage, to simply say sorry, I got it wrong.

Carl
• #### Carl Dalton

• 0
Mar 21 2014: Further Clarification 21st March

Key

Given a radius of e.g. 4 cm, when the 4 cm radius is added to its opposite radius of 4 cm, this will give a diameter length of 8 whole numbers/units.

Given a radius of e.g. 3•5 cm, when the 3•5 cm radius is added to its opposite radius of 3•5 cm, this will give a diameter length of 7 whole numbers/units.
……………..
Mental Imagery

Beginning with a circle containing 6 parallel rings, which extend from the centre of the circle, and each ring being 10 cm apart; it follows that the radius of the circle will be 60 cm in length; and when added to its opposite radius, the diameter of the circle will be 120 cm in length (Refer also to, Pi in Black & Yellow).

If we then take the single radius of 60 cm and rotate it 180°, it follows that its opposite radius of 60 cm, will also “simultaneously rotate 180° completing the circle.

Therefore as each 60 cm radius only rotates 180°, rather than 360°; it follows that the 60 cm radius x 180° = 10, 800 square cm’s; which is three quarters of the square, area of the 14, 400 square cm square.
……………

Therefore it follows that as 180° of rotation to the two radii of the same length, ensures an equality of area to the circle;

So it also follows, that each of the 6 rings will also possess an equality of area to their particular ring.

And the area of each one of the 6 rings will be rational by ratio, to each of the other 5 rings on a scale of 1 to 6.
……………

Given that there is an equality of the area to the circle, so it follows that when the area of the circle, is deducted from the equality of area to its square;

That the remaining four areas, of the four arcs of outer quadrant (corners) to the square, when added/combined together; will equate to an equal amount of area, that when added to the equal amount of area to the circle;

Be equal to the total amount, of square area to the original square.

Continued
• #### Carl Dalton

• 0
Mar 21 2014: 21st of March: Further clarification

Key: A radius of e.g. an equal 4 cm length, when added to its opposite radius of 4 cm of length

Will result in 8 whole numbers/units of diameter length.

A radius of e.g. 3•5 cm (3 1/2) of odd length when added to its opposite radius of 3•5 cm

Will result in 7 whole numbers/units of diameter length.

...................

Mental Imagery

Given a circle consisting of 6 parallel rings extending from its centre, and each ring being 10 centimeters apart

The radius of the circle will be 60 centimeters long (Refer to; Pi in Black & Yellow)

Therefore given that a single 60 cm radius rotates 180 degrees; and its opposite radius of 60 cm, is also "simultaneously" rotating 180 degrees.

It follows that the equality of the 360 degree circumferential length; relative to the whole number of 120 units of diameter length, will ensure an equality of area to the circle.

And the equality of the area, of each of the 6 rings;

Will be rational by ratio, on a scale of 1 - 6

.....................

Therefore given the square of a circles diameter length

When the equality of the area to the circle, is deducted from the area of the square

The area of the square remaining; will be 4 outer arcs of quadrant (corners) each equal in area to each other

And when the 4 are combined, this will give an equal area; that when added to the equal area of the circle

Will equate to the original overall area of the square.
• #### Carl Dalton

• 0
Mar 20 2014: Believe as you will, that is your right you stick with it because do you actually believe that you somehow have the power, to make me think like you because you nag like a child.

Nothing further from you will receive a response, so go bother someone else
• #### Carl Dalton

• 0
Mar 20 2014: Divide whole unit of 1 by 3 using decimals =

=3.33333333333333333333333333333333333333333333333333333333333333333333333

X 3

= 9.99999999999999999999999999999999999999999999999999999999999999999999999

Not a "whole unit" of 1

Archimedes cylinder had a circumference length of 3 whole units (diameters) consisting of 7 sub units

A single line is a single unit.

A circle is single symmetrical whole unit equal to 3 single units of diameter length

So let me make this clear if you cant get it, you cant get it, end of story; kids can get it, ordinary people get it; 8, 500 + in 118 countries, despite it being presented only in English get it, but you cant.

It seems utterly impossible! that anyone after reading from "A cube to its Sphere" does not get it; however it serves to define, the sheer strength of a belief, once it has become entrenched in the human psyche.
• #### Raymond Cavallaro

• 0
Mar 20 2014: Read your posts and mine again and you will see my answer is in my last post.

And about your 8500+ "ordnary" people, put this conversation entirely without cuts in your site and lets see who is really getting and who dont
• #### Carl Dalton

• 0
Mar 20 2014: Last time

Rational, a number that is equally divisible by another number

As in 21 over 7 divided by 7 = 3

Irrational, a number that is not equally divisible by another number, as in 22 over 7: 7 divided into 22 = 3.14 or 3 and 1/7

Symmetry of a circle, the length of a circle can be divided by any number, into that number of equal lengths to its overall length; as in 360 exactly equal lengths of degrees, or 3, 600 seconds to an hour, and 60 minutes to an hour.

When a round clock face tells you the time, it tells you the exact time, because the circular clock face has been subdivided into exactly 3, 600 equal lengths = seconds; which can not be achieved using 3 and a bit.

Archimedes problem was that his formula was in reality, 3 diameters and the thickness of the string, measured against that of a straight rule.

But as you cant get the fact that I mathematically built a perfectly symmetrical sphere, and empirically on a wood lathe; you simply are not going to get it and your wasting your own time and mine.

GOODBYE!
• #### Carl Dalton

• 0
Mar 20 2014: You have just defined yourself

Goodbye
• #### Carl Dalton

• 0
Mar 8 2014: 9th of March; Symmetrical Circles of Time

One 360° Hour is equal to;

60 Minutes x 60 Seconds = 3600 Seconds to the Hour
3600 Seconds ÷ 360° = 10 Seconds to the length of 1°

Therefore

1 Minute of 6 x 10 Seconds = 6°
5 Minutes of 6° = 30°
5 Minutes of 30° x 12 = 360° x 10 = 3600 Seconds to one Circular Hour

ONE METRIC CIRCULAR HOUR EQUALS

1 millimetre = 1° 10 seconds
6 millimetres = 6° 60 seconds – 1 minute
30 millimetres = 30° 5 minutes
5 minutes x 12 = 360° 60 minutes or 360 millimeters or 3600 seconds

Or One Metric Hour Measuring 36 Metric Centimetres

ONE IMPERIAL CIRCULAR HOUR EQUALS

1/12th of an inch = 1° 10 seconds
6/12ths of an inch = 6° 60 seconds - 1 minute - ½ of an inch
30/12th of an inch = 30° 300 seconds - 5 minutes – 2 ½ inches
2 ½ inches x 12 = 360° 3600 seconds or 60 minutes

Or One Imperial Hour Measuring 30 Imperial Inches

Question

Does: Einstein’s Magical Mystical Tour of the 4th Dimensional Time Zone, Exist in;

METRIC TIME or in IMPERIAL TIME

&

What Is The Differential Conversion Ratio, Between The Two Time Zones
• #### Carl Dalton

• 0
Mar 6 2014: John Mauren

Quote

Consider your simple black and white arithmetic disproved and negated.

Given the perfectly symmetrical sphere that was produced from a 60 x 60 x 60 mm base cube, using fractions rather than decimals.

Plus the irrefutable logic contained in "Pi in Black and Yellow", in regard to equality of areas

My simple black and white arithmetic has not been disproved, or negated; but rather proven beyond contention in math and logic.

However as I have noted a silence over the last 3 days from the virulent sceptics; this is to be expected, because everyone is so brave when they are part of a crowd/mob/gang; and very few indeed, will ever admit they were wrong.

No matter; the seeds are finally sown, and they will continue to grow

Arthur Schopenhauer 1788 - 1860

Quote: All truth goes through three stages; first it is ridiculed, second it is violently opposed, third it is accepted as being self evident.

Cheers Carl
• #### Carl Dalton

• 0
Mar 5 2014: 6th of March: Calculating the Area of A Ring

Given a yellow square card measuring 120 cm x 120 cm, and marked with a black circle measuring 120 cm high x 120 cm wide, and centrally a yellow circle measuring 60 cm high x 60 cm wide

In order to find the area of the black ring, the area of the central yellow circle, has to be deducted from the area of the black circle.

1. The area of the 120 x 120 cm yellow square is 14, 400 squares

2. The total area “contained” within the black circle is 14, 400 squares ÷ by 4 = 3, 600 squares x 3 = 10, 800 squares

3. The area contained within the central yellow circle is 60 x 60 cm = 3,600 squares, this area ÷ by 4 = 900 squares x 3 = 2, 700 squares

4. 10, 800 square area of the black circle, minus the 2, 700 square area of the central yellow circle = 8,100 squares to the square area of the black ring.
• #### Carl Dalton

• 0
Mar 3 2014: Ariel : Pi Black & Yellow

We have two yellow square cards each measuring 120 cm x 120 cm

Card 1. Has a black circle measuring 120 cm high x 120 cm wide, and the square card has been cut into 4 equal squares, each measuring 60 cm high x 60 cm wide

Each 60 x 60 square card holds one quadrant of the yellow square, and one quadrant of the black circle

Card 2. Has been cut into 4 equal 60 x 60 cm square pieces, each square has a black circle 60 cm high x 60 cm wide

A. Black Areas
1. All black areas have an equal area to each other
2. Any number or type of black area combined will give an equal area
3. All black areas combined will give an equal area

B. Yellow Areas

1. All yellow areas have an equal area to each other
2. Any number or type of yellow area combined will give an equal area
3. All yellow areas combined will give an equal area

C. Sum
1. All areas have an equal area
2. Any number and any combination of black and yellow areas, will give an equal area
3. All black and yellow areas combined, will give an equal area
4. All areas of the two cards combined, will give an equal area (288 squares)

Logic:

1. All of black and yellow areas of circle and square contain an equality of area.
2. When an equal amount of area is deducted from an equal amount of area, it leaves an equal amount of area.
3. Pi has a greater sum of inequality to its area, than that of the lesser sum of equality to the area of the circle.
4. Pi is a mathematical infringement into the area surrounding a circle
5. Pi is approximate to the circle, but an area of the yellow square

Sum: Case Proven

Pi is an inequality, mathematically inducted into the Archimedean formula

Refer to "From the Cube to its Sphere"; which received a thumbs up, from my major detractor.

As to your inference that I am an idiot; I suggest you apply such insults to those sub cerebrally vacuous idiots, who wasted time and their weak energies, posting inane comments, and insults during this conversation
• #### Raymond Cavallaro

• 0
Mar 20 2014: It is all right until Logic-3

With Pi you get exactly the same result
• #### Carl Dalton

• 0
Mar 2 2014: It seems I have a thumbs up (from a major detractor) relative to my latest post, namely the "non approximation" of a sphere; so I will take this as a positive, and add in the extra text that could not be fitted into the previous post, and move on to ovals and ovoids.

A. The Cylinder is three quarters of its Cube
B. The Sphere is three quarters of its Cylinder
C. The Sphere is nine sixteenths of its Cube

Note; the reason why there is no approximation when creating the sphere on a wood lathe, is because there is "no line/perimeter of approximate separation" but rather the exact separation/deduction of one mass into two masses. And this is as it should be with the circle, the exact area of the circle

Area and volumes of symmetrical ovals and ovoids

Contained space, volumes, and areas have dimensions of length, breadth, diagonal, and perhaps also curvature, and so from a geometric perspective, they can be taken to be geometrically interchangeable.

Therefore the volume of air within a symmetrical ovoid can be equated to the same amount of air, within a sphere, that has been compressed downwards to create the symmetrical ovoid.

And it follows that the area contained within an oval, can be equated to the same amount of area within a circle that has been compressed downwards to form the oval.

Given a circle with a diameter of 6 cm, there will be 36 sq cm to the square ÷ by 4 = 9 x 3 = 27 sq cm to the circle.

Given an oval 3 cm high by 12 cm long; 3 x 12 = 36 sq cm to the rectangle ÷ by 4 = 9 x 3 = 27 sq cm to the oval.

Therefore as a circle is ¾ that of the area of its square, & a symmetrical oval, is ¾ the area of its rectangle, it follows;

D. The cylinder of the rectangular cuboid, is three quarters of the cuboid
E. The ovoid is three quarters of its cylinder
F. The ovoid is nine sixteenths of its rectangular cuboid
• #### Carl Dalton

• 0
Mar 1 2014: Bryan Maloney

• #### Carl Dalton

• 0
Mar 1 2014: 2nd March: A Cube to its Sphere

Beginning from a wood cube measuring 6 x 6 x 6 centimeters, we have to imagine that we are turning it on a wood lathe, to produce a cylinder by removing 4 sides & ¼ of its mass. The cylinder is then replaced lengthwise, to remove the two circular faces, & ¼ of its mass to create the sphere.

12 steps to the Sphere

1. Measure the Cubes height to find the length of Diameter = 6 cm

2. Multiply the Diameter by itself, to obtain the Squares length and Square Area, = 24 cm and 36 sq cm

3. Multiply the Square Area by the diameter to obtain the Cubes Cubic Capacity = 216 cubic cm

4. Divide the Cubes Cubic Capacity by 4 to obtain ¼ of the Cubes Cubic Capacity = 54 cubic cm

5. Multiply the ¼ Cubic Capacity by 3 to obtain the ¾ Cubic Capacity of the Cylinder = 162 cubic cm

6. Multiply the Area of one Face of the Cube by 6 to obtain the Cubes Surface Area = 216 sq cm

7. Divide the Cubes Surface Area by 4 to obtain ¼ of the Cubes Surface Area = 54 sq cm

8. Multiply the ¼ Surface Area by 3 to obtain the ¾ Surface Area of the Cylinder = 162 sq cm

Cylinder to its Sphere

9. Divide the Cylinders Cubic Capacity by 4 to obtain ¼ of the Cubic Capacity = 40 ½ cubic cm

10. Multiply the ¼ Cubic capacity by 3 to obtain the ¾ Cubic Capacity of the Sphere = 121 ½ cubic cm

11. Divide the Cylinders Surface Area by 4 to obtain ¼ of the Surface Area = 40 ½ ″ sq cm

12. Multiply the ¼ Surface Area by 3 to obtain the ¾ Surface Area of the Sphere = 121 ½ sq cm

Confirmation by weight using a "16 x 16 x 16 cm cube" weighing 160 grams

Given that a 16 x 16 x 16 Cube weighs 160 grams, prior to being turned on a wood lathe to remove 1/4
of its mass

A. The Cylinder will weigh 120 grams
B. The wood shavings will weigh 40 grams

Given the Cylinder weighs 120 grams prior to being turned on the wood lathe to remove 1/4 of its mass

A. The Sphere will weigh 90 grams
B. The wood shavings will weigh 30 grams

Archimedes Principle for volumes
• #### Carl Dalton

• 0
Feb 28 2014: Evan S and co

This cannot be classed as being equal to the diameter/extent, that lies between sarcasm and wit; and therefore is not of the full circle (IQ).

Grow up
• #### Carl Dalton

• 0
Feb 28 2014: 28th of February

Oxford English Dictionary

Approximate: "fairly" correct or accurate; "near to" the actual (the approximate time of arrival; an approximate ''guess''!!!)

Therefore Pi "is not" correct or accurate; and only near to the actual (What) and of no more mathematical value "Than a Guess".

So what are we supposed to guess that Pi is "Approximate to" = "Near to" if it is not 3 diameter lengths???

Because as Pi is simply "" 3 + a bit ""!;

If you get rid of the bit; what do you end up with if not 3???

But it seems all of the worlds mathematicians are unable to get rid of that extra bit, and are unwilling to admit that if you remove its addition, you are left with 3.

For those who are open minded, and interested in examining all of the evidence presented, rather than addressing a single or odd post; I suggest copying the evidentiary posts, and pasting them together.
• #### Carl Dalton

• 0
Feb 28 2014: Hi Ariel

Re Equations and your mention of Einstein

E = mc2

E = mc2 : States that Energy is equal to a (1) unit of Mass, multiplied by the Speed of Light Squared.

However this is totally impossible; because 1 unit of Energy, is not equal to 1 unit of Mass.

1 unit of Energy; is 1 unit of substance/energy/matter and nothing more

1 unit of mass; is equal to the quanta (density) of its energy content + the additional force/weight (Energy) of Gravity (G)

Therefore it follows

Energy + Gravity = E + E

And 1 unit of Matter (Energy) + the Weight (Force = Energy) of Gravity; is greater than the value of 1 unit of Energy/Matter.

Therefore it also follows

The "multiplication" of an unspecified density/quantity/value of Energy; plus an unspecified density/quantity/value of Gravitational Energy;

By the speed of light as measured within Earth's gravitational field "and then squared" does not equate to the amount of energy; that is contained within any given amount of mass

Or the speed that the photon minus gravity would achieve in interstellar space .

Speed of Light

The speed of light is not constant, it travels faster through a vacuum than air "density", faster through air than water "density", faster through water than glass; therefore it will travel far faster through interstellar space (Density = Quanta of Energy = Gravitational Quanta/Power/Pull of a Particulate or en-mass)

E = mc2 simply means that one unit of Energy is equivalent to one unit of Mass; multiplied by the straight A to B linear speed of light per second; squared, which is 90, 000, 000, 000, 000 kilometers per second.

However as electromagnetic radiation/light, is perceived to travel in the form of the upper and lower curves of a wave length (IMO spirals);

How does the squaring of the straight linear A to B length; relate to the speed the photons are actually traveling , over the "greater distance" of the upper and lower curvatures, of the none - straight linear, A to B distance
• #### Ariel Ramirez

• +1
Feb 28 2014: Sir, I respectfully implore you to read more in the subjects of EVERYTHING you know. So you know, just to check. You have a nasty habit of assuming too much and assuming that what you know and what you understand things to be is correct. To err is only human. Better to be an idiot once and learn I believe. :) For example, an elementary understanding of math would show that E=MC^2 does not in any way shape or form claim that 1 unit of energy is equal to 1 unit of mass as you say it does. You also have a habit of being increasingly off topic as I only mentioned Einstein as an example of proving what was previously thought to be correct as wrong, but you proceeded with a whole lecture of your misinterpretation of sir Einsteins work. Please sir, just review your studies.
• #### Carl Dalton

• 0
Mar 1 2014: E is the energy produced when mass is converted into energy; therefore I could have used the term one iota of mass, one lump of mass whatever; I used the definition as given on page 82 of "Infinity In Your Pocket" written by Mike Flynn.

No one knows what energy is at a fundamental level, other than it is a substance; and it follows substance + motion = force = energy/matter

Matter = Energy
Gravitational force = Energy

And mass equals both (And G is variable, e.g. Greater re Jupiter than on Earth)

You chose to go off topic not I; and you chose to use Einstein as an example of proving what was previously thought to be correct as wrong; poor example as you assumed that I accept Einstein's theories as being correct which I do not.

No more so than I accept that the "atomic structure" of a lift accelerating in space, can travel faster than a beam of light being shone across the "inside" of the atomic structure of the lift, and bend it.

Especially as the lift, the atomic structure of the torch, and the beam of light are accelerating in the same direction, at the same speed.

Because please correct me if I am wrong; was it not Einstein who stated categorically, that nothing can travel faster than the speed of light/electromagnetism? And most certainly atoms cannot travel faster than photons, regardless as to the amount of acceleration impressed.

Also was it not he that said quote; If the facts do not fit the theory, change the facts

Well a fact is a fact; and a theory should be based upon the actual and factual/empirical; not assumptions or changing or ignoring the facts. namely the basic laws of physics.
• #### Carl Dalton

• 0
Feb 27 2014: 28th of February: Euclidean and Sumerian Accord

A circle is infinitely symmetrical, and can be sub ÷ into an infinite number of equal and identical lengths, by any whole number.

All lengths/radii extending from a circles centre, to its perimeter are identical, relative the quanta (measure) of their length.

Two identical and equal quanta lengths of radius when added together, give an equal quanta length of diameter.

Two identical but unequal quanta lengths of radius when added together, give an equal quanta length of diameter.

Therefore as it is, the circles radius that serves to dictate the equality of quanta to the circles diameter length, and dictate the equality of quanta to the circles perimeter length, and both are of the same source;

It follows that the lesser equal quanta length of diameter; will equally divide into the greater equal quanta length, of the circle.

Relative to both Euclidean and Sumerian geometric principles

A circle is infinitely symmetrical in nature, because it is in effect a cross section of a sphere; and therefore if we look at a round protractor, we can see that all three dimensions of lateral, vertical, and diagonal, are contained/exist within the circle.

Therefore all three dimensions of radiation, extending outwardly in all directions from the centre of the circle, also exist as such; within the fourth dimension of the curvature of the sphere, or more concisely, the sphere of influence/radiation of a particle of energy.

However in reality relative to the sole spatial being of a sphere in empty space, the outwardly directed radiations from the centre of a sphere; do not possess any directions of latitude, longitude, or diagonal; as a sphere does not possess any directions of north, south, east or west.

Linear geometry mimics nature, nature does not mimic linear geometry.
• #### Carl Dalton

• 0
Feb 25 2014: My calculations have no errors categorical; SIMPLE ARITHMETIC does not allow for this, it is self evident - black and white

Everything/substance/energy/ matter "is not" divisible by linear decimal math;

22 identical mirror image parts of a symmetrical circle divide by 3 = 7•3333333333 recurring

7•333333333 multiplied "Back by 3" = 21• 99999999999 recurring

Which is not the whole of the original circle consisting of 22 mirror image parts of the "originally" symmetrical circle

Rather than 22 identical mirror image parts, of a symmetrical circle divide by 3 = 7 & 1/3rd

7 & 1/3rd multiplied "back by 3" = 22 mirror image parts of the "original" symmetrical circle

And you can keep falsely claiming to have disproved it, that does not alter the fact that you have not done so, because according to and by the use of simple division and multiplication; the results are absolutes.

And while using the square of the radius x 3 & 1/7, gives an approximate area of the circle; the square of the radius x 3, gives the exact area of the circle which is three quarters of the square

And you have been given four different methods, one used by the Sumerians which all give exactly the same result; therefore the result of the Sumerian method supports/concurs with the same three results of the methods I used to obtain them, and provided; and the results of those three methods support/concur with the same result I obtained by using the Sumerian method; and you cannot deny or change that fact.

However regardless of plain english, simple arithmetic-you will continue to believe as you will, and it really does not matter what empirical evidence is provided; it is totally impossible to convince your totally closed mind; and I am not interested in doing so.
• #### Raymond Cavallaro

• 0
Mar 20 2014: 1/3 = 0.3 + (0.1)/3
0.3 is the answer, 0.1 is the rest of the division

you can go on
1/3 = 0.3 + (0.1)/3 = 0.33 + (0.01)/3 = 0.333 + (0.001)/3 = 0.3333 + (0.0001)/3 = 0.33333 + (0.00001)/3

in the end if you say 1/3 = 0.33333... is wrong, you are missing the rest of the division (0.000...01)

So X divide by 3 multiplyed by 3 is always X
Even if
X = 22
Lets say:
3Y = X
Y = 22/3
22/3 > 7.3333...
Y > 7.3333...
3Y > 21.9999...
X > 21.9999...
22 > 21.9999...

360 is a convention, you could divide the circle by any amount, like percentage
Pi radius = 180 degrees = 50 percent
So in percentage, the unit that is dividing the circle is 100

You can divide anything for any amount, that is math

What is everyone saying to you and proving to you throught facts and pointing your errors
is that there is no error in your math, there is error in your logics and concepts

And i dont know if you are doing it on purpose to get us tired or to not admit you are wrong but you are trying to twist every concept to fit your logic that doesnt fit the reality

you have good math solving but bad conceptual understanding over it

stop repeating your posts all over,
read and understand our posts, and you will see everybody understand what you did
you should at least do what you ask us and read and understand our posts
And if you are going to ignore us and just dont wanna know, why did you put this topic in the forum

And read your critics to us because it fit perfectly to you
• #### Carl Dalton

• 0
Mar 21 2014: This really is going to be the last time

Descartes

X Y and Z are symbols of “unknown quantities”

Fractions are symbols of proportion, relative to the known quantity of a whole unit (Number/Symbol) of reality, e.g. 1 apple pie is one whole unit of something, that is real (mass/reality)

Therefore divide 1 unit of apple pie by 3 with a knife, you have 3 x 1/3 pieces of the apple pie x 3 = the whole apple pie (Reality).

Divide 1 apple pie by 3 using fractions, you have 3 x 1/3 rds of the apple pie x 3 = one whole apple pie = 1 whole unit = reality.

You cannot in reality, cut 1 whole unit of apple pie with a knife, into 3•333333333333333 pieces, and hypothetically if you could; on putting the 3 pieces back together again, you would only get 9•999999999999999 of the original apple pie.

But be assured your so locked into the decimal system; and the decimalization of 22/7, you’re never going to get it.

End of story
• #### Carl Dalton

• 0
Feb 25 2014: Precisely Pi has been proven not to equal but rather approximate to 3;

The axiomatic evidence as to a circle being equal to three diameter lengths has been presented and it is self evident; but not to those who are unwilling, or unable to examine the evidence with an open mind and accept the evidence

As Ken Robinson quoting Benjamin Franklin said: There are three types of people, those who are immovable, those who are movable, and those that move.

Somehow you have the idea that it is your place to convince me that I am wrong, and that you are right; whereas I am not interested in convincing you that you are wrong or right; I am merely responding to your attempts to try and convert me to your way of thinking "Which is never going to happen".

I have put the evidence out, so that others can make up their own minds, you joined the conversation of your own choice. I did not ask you to.

Quite simply believe whatever you like, that is your right; as it is the right of everyone else including myself, I am not trying top change you, and I suggest you stop trying to change me, because as I said "it is not going to happen.

However I will post this once more: Pi is 22/7 as an improper fraction, "using a calculator"

22 ÷ by 7 = 3•142857144285

3•142857144285 x by 7 = 21•99999999999 recurring

Which is closer to the original number 22/Circle, than the original division of 22 by 7

Cheers Carl

• +1
Feb 25 2014: You misunderstood, so I'll say it one last time.

Mathematics isn't a matter of not believing you. Its a matter of presenting your proof and examining it for errors. If there are no errors, its true, plain and simple.
Your calculations had errors, as I've pointed out bellow--you used the thing you were trying to prove as part of your proof. Therefore, the proof is inadmissible.

Martyring yourself in the name of this cause doesn't make you right, it just exposes you to ridicule for no good reason.
• #### Ariel Ramirez

• 0
Feb 25 2014: Carl Dalton
You seem like a smart guy, and i respect you for that. As such, it would be more respectful for not only you but also everyone else to remember that there is no such thing as truth in science. Science is evidence based and if your evidence is as powerful as you believe it to be then present it in a scientific paper instead of open fora such as these. Have it peer reviewed and studied and debated and who knows? It took sometime for Newton to be proven wrong by Einstein, but when the proofs were down no one could contradict the evidence. If your math was right and the world was wrong, especially regarding something as important as circles, then I'm sure you will receive nothing short of a Nobel Prize, and I will be with the crowd clapping.
• #### Carl Dalton

• 0
Feb 28 2014: Hi Ariel

Sorry have been busy, but will get back to you here is my latest post

Cheers carl

28th of February: Euclidean and Sumerian Accord

A circle is infinitely symmetrical, and can be sub ÷ into an infinite number of equal and identical lengths, by any whole number.

All lengths/radii extending from a circles centre, to its perimeter are identical, relative the quanta (measure) of their length.

Two identical and equal quanta lengths of radius when added together, give an equal quanta length of diameter.

Two identical but unequal quanta lengths of radius when added together, give an equal quanta length of diameter.

Therefore as it is, the circles radius that serves to dictate the equality of quanta to the circles diameter length, and dictate the equality of quanta to the circles perimeter length, and both are of the same source;

It follows that the lesser equal quanta length of diameter; will equally divide into the greater equal quanta length, of the circle.

Relative to both Euclidean and Sumerian geometric principles
• #### Ariel Ramirez

• 0
Feb 28 2014: Yes well I see your point. It does seem like the mere fact that the circle is symmetrical should also indicate that its diameter is a whole number. But. Have you tried looking at the many proofs of pi and try to look at where all the others have got it wrong? I believe that many mathematicians were as baffled as you because they couldn't make the diameter of a circle exactly three. The thing about math is, one equation doesn't really cut it, at least not anymore. There are multiple proofs to pi, spanning mathematicians in hundreds or even thousands of years. I'm not saying you're wrong. But, if you're right, and they're right, but you say different things, then who is wrong? I think we need more accurate proof than logical reasoning when it comes to math. for example, using math I can prove that girls are evil.
Time is money. (Time = Money)
Girls are worth the Time and Money (Girls = Time X Money) -> (Girls = Time^2) or (Girls = Money^2)
Money is the root of Evil (Money = square root of Evil) -> (Money^2 = Evil) + (Money^2 = Girls) = (Girls = Evil)
This is an old silly proof which you are probably familiar with. Its just to illustrate a point that as languages, we can use math or logic to say what we want to say. As such, we need more stringent proof that a circle's diameter is 3 other than the logical reasoning you provided. Cheers.
• #### Carl Dalton

• 0
Feb 28 2014: Hi Ariel

I will get back to you but pretty busy, so quickly: Time = Money this is based on an assumption not reality, as are so many equations and theories.

Money represents the conversion of the product of the expenditure of energy = motion = force = work; via a transaction into a portable form of energy, in the form of a promissory token or note (IOU), that can be sub divided into smaller units of portable units of portable energy called small change.

Time is money is rather the concept and foundation stone, of the slave driving mentality of capitalism; which in the early centuries of its " Greco Roman (Fascist refer to Fasces symbol of Roman authority) founders, rather than the least amount of money being paid for work carried out today; then a minimum amount of food and a whip was used to make them work faster in order for the slave to be more productive and profitable. Hence it is the fascistic concept that is evil, and nothing whatsoever to do with women.

But then again perhaps your right, as given that the mother of Romulus and Remus was supposedly a wolf; then it would follow that the Romans who tortured and crucified JC after he drove their mates the Greek merchants/capitalists, and slavers out of the temple, and called them a pack (Den) of thieves; were evil sons of bitches.
• #### Carl Dalton

• 0
Mar 6 2014: Hi Ariel

Apologies for not answering this post earlier, however as you know I have been dealing with flack (yours included), which takes time and thought.

Smart as compared to who or what? The amount of knowledge and intelligence that I possess, is infinitesimal, as compared to the infinite scope of the infinite depths of the abyss, of my own ignorance; and for every question I think I may have solved, or after much re-examination I am satisfied I have solved, so many more arise to replace it (e.g. how the hell can a straight line, measure the same length as a curved line? Interesting, fascinating, unbelievable, all you can do is put it to the back of your thoughts, and not obsess about it)

Scientific evidence was originally empirically based but no longer, as Einstein saw to that, with his philosophy of “If the facts (evidence) do not fit the theory (idea) change the facts. Einstein used his friend’s notes in order to pass his exams, and later in their finals, he and his wife Maleva Malik got exactly the same score, which was one mark under a pass (what a coincidence). However despite this he was given a pass, but she being a woman and of peasant stock, was failed.

What is interesting, is that having treated her more like servant than wife once he had qualified (?) as a physicist, when he won the Nobel Prize Maleva went to visit him, and following this, he gave her all of the Nobel prize money, but not before laundering it through several banks to cover it up. Why? Because it was Maleva who was the brilliant student not he. And what would history read like today, if she had become the Einstein and not he?

As to the world that exists behind the walls of authoritarian academia, it reminds me of the lyrics of the Simon & Garfunkel song “I am a Rock” being indeed a “Fortress Deep and Mighty” and I am glad to say, that I am not part of it. As to plaudits and prizes, the world can keep them I prefer personal anonymity, and my work is my intellectual property
• #### Carl Dalton

• 0
Feb 24 2014: History depends on which books you read, and how you interpret them, as you should be aware

As to engineering; e.g a piston and a cylinder, as piston and cylinder are both measured using pi then both work in synchrony.

In fact a friend of mine gave his brother who is a diesel engine mechanic a copy of my work; and so he decided to regrind the pistons, and cylinders of a spare car he had to a 3 - 1 ratio; result greater compression.

Can you imagine the millions of life hours that would be saved each day world wide, and not be wasted on both using and teaching Pi, and thus allowing those life hours to be used on increasing human studies and progress in other academic, and technological areas (Sadly also ballistics) , it would be both universally beneficial and phenomenal.

Do you actually think I relish putting this forward, in the full knowledge that I will be subject to ridicule and abuse as with the previous comment; and based on human history; more likely than not destroyed; if so you have far more faith in humanity than I do, and it grows less each day.

Cheers Carl

Addendum: Quote: Arthur Schopenhauer 1788 - 1860

All truth goes through three stages; first it is ridiculed, second it is violently opposed, third it is accepted as being self evident.

And sadly, I expect the second to be inevitable, not as to the evidence but rather myself, and that is soundly based in life experience; and as a result I do constantly ask myself, why the hell do I bother.

• 0
Feb 25 2014: Hate to break it to you, but Pi is used in a lot more then circles.
Practically everything relying in Sine and Cosine functions, for example, and those two crop up anywhere and everywhere. Including geometry. Everything from simple mechanics to wave theory to electricity relies on it.

Truth may find itself ridiculed in most fields when it first seems unlikely, but math, being an axiomatic system, is actually the one place where that's not supposed to happen. You're either right or you're wrong, and unlike the sciences, its possible to definitively prove it one way or the other. Pi has been definitively proven to not equal 3--it might have been empirical when the Greeks did it, but we have newer, mathematical proofs which are indisputable.
• #### Carl Dalton

• 0
Feb 24 2014: Bryan Maloney

Thank you for your mathematically unsupported opinion, stemming from two thousand years of Greco Roman impressed belief; extending from pre plagiarized geometry prior to Alexander and his Generals destruction of the far more advanced Babylonian Civilization; and the loss of the greatest concentration of knowledge of the ancient civilizations, with the burning of the Alexandrian Museum in Egypt.

By ignorant closed minded individuals such as you, en-mass; I suggest you look in the mirror; and if you do not possess anything that is constructive, pertinent, or empirically valid to put forward in the conversation; take your infantile abuse elsewhere, where you may find it more effective.

As to my being looney; I suggest you read the novel "Catch 22" because in this crazy world of ever increasing violence and mental illness; I am always questioning and scrutinizing my own mentality, and sense of reality, in relation to the realities of this world and the Universe.

In sum Get Lost, oops sorry, you already are!

• 0
Feb 24 2014: Actually, Alexander conquered the Persian empire, which themselves conquered Babylon in its culmination of decades of decline. The Greeks also adopted more eastern customs then they destroyed. They also had better things to do then to suppress mathematicians.

I'm afraid to say your grasp of history is as poor as your grasp of arithmetic.

You know, the sheer amount of precision engineering that wouldn't work if Pi actually equaled 3 boggles the mind. The lot of our modern technology wouldn't work on account of design flaws. Seeing as you're reading this text through an electronic device which was doubtless designed with Pi somewhere along its engineering process, I'd say we're safe.
• #### Bryan Maloney

• 0
Mar 1 2014: Evidently, you don't know you're a loony. At least you're funny.
• #### Bryan Maloney

• 0
Feb 24 2014: You're a loony, did you know that?
You also have no understanding of math.
• #### Carl Dalton

• 0

The sheer scope of your hubris is almost as unbelievable, as is your “falsehood” in claiming to have proven the “simple – elementary – basic” arithmetic involved to be wrong; which is totally impossible; and more especially in your case, as you state that you are unable to read, and understand, simple arithmetic written in paragraphs. So pray tell me, how is it possible for any person to disprove, that which they do not understand?

And indeed if this were true, then you would be smarter than all of the 8, 200 + persons in 117 countries around the world, who are logging on to my web page; and all of the Sumerian master geometers and mathematicians of 3, 500 years ago, who as with the modern ages, would have taken several previous centuries, to reach their conclusions.

Axiom: “A Circle is Perfectly Symmetrical”

Therefore, The Circle can be subdivided by any whole number; into that number of “Equal Parts to its Whole”

Ergo: The Sum of the Circles Equal Parts, are the sum of its “Symmetrical Length”.

Ergo: The sum of "Three Equal Diameter Lengths, equates to the sum of the "Circles Symmetrical Length".

Axiom: The four sides of a Square are Equal

Therefore one side of a square used as a diameter, and rotated 360°, will produce a circle of the same height, and the same width of the square, in 360° of direction; and the sum of three diameter lengths; each being of the same length, as the four sides of the original square.

As to not being worth the hassle; it is far simpler and faster to multiply a diameter by 3 to gain an exactitude; than multiply it by Pi to gain an approximate error.

If that is not simple enough for you, too bad; get over it

Cheers Carl
• #### Carl Dalton

• 0
Feb 23 2014: Indeed you made me realize; through no fault of your own, but rather the education system; younger generations, have lost the ability to read and comprehend written arithmetic.

And on my part, I find it difficult to comprehend that you are unable to; rather than trying to read the paragraphed arithmetic in a mathematical format, to read it "slowly" as the written word in sentences of english, and "allow time" for the sense of the written words, of each sentences, to gel in your mind before moving on to slowly read the next sentence.

The problem today is an input of far too much information (most of it useless commercial based media/junk non sense) distracting, and being crowded into the mind from all directions simultaneously; and thus preventing the mind from being able to rest and absorb, and understand what has been written; because finding the time to "read rather than quickly scan written works" has become so difficult.

This is further confirmed by the fact that the speed which both of you and Fitzies replies were written and posted, wassurprising and unexpected.

I know this too be true, because the time consuming physical banalities and chores of every day life, are a distraction: You mentioned mathematicians being brought to near tears by the stress of their mental exertions; well it was a relatively simple matter to suddenly realize while measuring a tube with a micrometer, that the 1 & 1/2 inch diameter of the tube, equated exactly to a circumference of 4 1/2 inches or 9 x 1/2 an inch. As opposed to many hundred of hours spent over three years; working out the method for calculating the surface area and volume of a sphere. And then finding a method for diagrammatically presenting it for ease of understanding, using a wooden cube and a wood lathe, in order to convey an empirically visual and demonstrable means of understanding.

Still I have some 8, 200 followers in 117 countries and 224, 000 + hits, so am making progress

Cheers Carl

• 0
Feb 23 2014: That's not the problem actually. The problem is when your arithmetic is proven wrong and you simply ignore the mistake and push onward.

Besides, reading equations as paragraphs isn't exactly what I call a useful skill. Its sort of like insisting to learn how to read backwards--it just doesn't come in handy enough to be worth the hassle.

• 0
Feb 23 2014: Well, I've given up. There's no talking sense to some people.
• #### Carl Dalton

• 0
Feb 23 2014: Not so

You will not convince me, and I will not convince you; no matter as I said the information is out there for others to consider, and form their own opinions.
• #### Carl Dalton

• 0
Feb 23 2014: No and they do not apply it to the 12 base and 12 vertical right angle; doubt it try 24 base and 24 vertical and its out by 4 squares and so on.

Using a diagram on 1 cm graph paper using a 12 base and 12 vertical right angle to represent one quarter of a 24 diameter circle; and then draw in the 17 hypotenuse between the top of the vertical and lateral base line.

Then from the centre of the circle (90 degree angle) it measures 8 and a half squares "diagonally" to the hypotenuse line;

Repeat the same in the opposite direction to the hypotenuse, and the distance between the two opposite hypotenuse is 8 and a half + 8 and a half squares = 17 diagonal squares.
• #### Fritzie -

• 0
Feb 23 2014: Regardless of your pick for the length of the two legs, you will find the area of the square on the hypotenuse will always equal the sum of the squares on the legs.
• #### Carl Dalton

• 0
Feb 22 2014: Fritzie

It is indeed a pity I cannot provide the diagrams here, as these would also include working from a diameter up to the surface areas and volumes of both a cylinder, and sphere.

However I have noted on the internet people asking how many degrees there are to a sphere, and no one can provide an answer.

So based upon 360 degrees to the circle; here is the method, relative to latitude and longitude, for anyone who is interested.

Looking at a circular protractor with the 0/360 point at the top; there are 180 degrees extending from the 0/360 point down to the protractors 180 degree point; now take the protractor and rotate it 360 degrees, and each of the 180 degrees rotates 360 degrees; therefore there are 360 x 180 degrees of latitude and longitude to the sphere = 64, 800 degrees, although quite obviously each circle of degrees, grows shorter in length distal to the spheres equator. And in reality considering and including diagonal dimensions in equality of surface area, each degree of its self, would belong to 360 circular dimensions; which is quite mind boggling.

In other words, I think jam jar lids, do not possess any more authenticity than Archimedes bit of string; and I am neither a student nor a child.
• #### Carl Dalton

• 0
Feb 22 2014: Fact Pi is an Approximation to the 3 diameters within it

Therefore if pi is an accurate approximation as you insist, which is a contradiction in terms

Then strictly hypothetically speaking

Mathematicians accept and state that Pi is an Approximation

Therefore as the 3 diameters in Pi, are approximate to Pi

So it follows as both 3 and Pi are merely approximates;

And neither possesses an actual and factually defined mathematical value, of magnitude/measurement/quantity;

Both are equally just approximates' and as such, one approximation is worth no more than the other; because a near miss is still a near miss regardless of whether it is an inch or a mile, or a centimeter and a kilometer.

It is a simple fact; that once a belief is ingrained within the human psyche, the psyche will not be convinced otherwise regardless of self evident facts, or any amount of persuasion.

And there are tens if not hundreds of millions like you and Fritzie, who will not be convinced regardless of what I say: And therefore it is not my aim to convince you or those millions of others, because it is impossible.

But rather to place this information on the record and out there, and so allow others who use simple arithmetic in their daily lives, and have no vested interest in promoting, or in defending the Approximation of Pi;

To make their own decision, as is their right.
• #### Carl Dalton

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Quote

If you don't believe me, grab something circular, measure out its diameter, then use a known length of string to measure the circumference.

"Its not a terribly accurate" method

(the string stretches and never follows the perimeter exactly),

but it was good enough that the ancient Greeks realized it was

"three and a bit" as opposed to straight up 3

Indeed! APPROXIMATE' to the actual length of the 7 centimeter/measurement units diameter; cylinders actual circumferential length which it cannot accurately measure: Because when the string is measured against a straight ruler, it is the outer stretched circumferential length of the thickness of the string that is being measured, not the constricted inner thickness lying next to the cylinders surface,

And I am sorry I would have liked to be able to provide the accompanying diagrams, as you are right diagrams do serve for greater clarity.

As to decimals relative to the improper fraction of Pi

Using a calculator ÷ 22 by 7 = 3•14285714285

Then multiply 3•14285714285 by 7 = 21•9999999999

Closer to 22 but you cannot get the whole 22 back

However 22 ÷ 7 = 7 & 1/3rd x 3 = 22; and you have the whole number back again.
Also "Mathematics is said to be an Exact Science" so why is an "Approximate to 3, more acceptable than 3"

Fact anything "Symmetrical" can be divided into equal parts, by a whole number; and a circle is perfectly symmetrical.

Here is another anomaly for you to play with.

There are 367 proofs of the Pythagorus theory which also goes back in time to the Sumerian age, however;

Given a right angle with a base 12 cm long and a vertical of 12 cm long; the hypotenuse will measure 17 cm, and the square on the hypotenuse will have 289 squares;

While the two squares on the other two sides will have 144 squares each, a total of 288

One square less; so what do I accept, what I have been told; or the proof of simple arithmetic?

I will stick with simple arithmetic

Cheers Carl. .

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Feb 22 2014: If the proof doesn't match with your arithmetic, then either the proof is wrong, or you've made a mistake on the arithmetic.
Seeing as how these proofs are fretted over by math majors onto a point which would make a normal human being break down crying, I find the second option more likely.

As for Pi, there is a reason they call it a decimal approximation. There is actually a proof showing that it can't be perfectly expressed as either a decimal point, or even a fraction of any two rational numbers. An irrational number they call it, there's an infinite number of them, like the square root of 2.
A calculator uses a decimal approximation for the simple reason that an approximation approaching say, 1/100000000 of Pi is good enough for any practical purpose, even if a mathematician will scoff at it for not being exactly right (mathematicians like to pretend they live in a perfect world where all measuring devices are perfect and there are no unknown variables).
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Feb 22 2014: The hypothenuse does not measure 17 by the Pythagorean theorem. it measures root 288.
• #### Carl Dalton

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Feb 23 2014: Using Decimals not diagrammatically squares

Reality we take "1 whole unit" an apple pie, weigh it and then cut it into three equal pieces, then weigh it and we still have the same amount.

Taking the same 1 whole unit, and mathematically dividing it by 3 we have three fractions of 1/3rd, and if we then multiply 1/3rd by three we have 1 whole unit of 1 apple pie.

However if we use a calculator to mathematically divide 1 whole unit of apple pie by 3 it gives •3333333333

If we then multiply •333333333 to regain our whole unit of 1 apple pie; we only get •999999999 of the pie back.

Because fractions are based in reality, and decimals in virtual reality, which is why computers crash.

Everything in the Universe/Reality/Energy/Mass is not made up of 10 linear parts

Numbers applied to anything should represent the qualities and quantities of value of the thing they are being applied to; not an arbitrary and universal value of 10.
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Feb 23 2014: But the theorem says that the sum of the areas on the squares of the two sides adjacent to the right angle equals the area of the square on the hypotenuse. The length, then, is the square root of that.

That is what the 367 proofs prove. They make no claim about decimal approximations.
• #### Carl Dalton

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Feb 22 2014: Fritzie

Quote: All truth goes through three stages; first it is ridiculed, second it is violently opposed, third it is accepted as being self evident.

Arthur Schopenhauer 1788 - 1860

You obviously fit the first category, and given more than two thousand years of belief, and tens if not hundreds of millions of believers, and the savage history, and ongoing savagery of humanity; the second category may well be pending; and the third category, I may not be around to witness.

Disprove the "SIMPLE ARITHMETIC" if not, stop wasting space, both here, and there where you are.

And certainly this is not a responsible, unbiased, or arguably ethical behavior, on the part of a TED host.

Cheers Carl
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Feb 22 2014: I in no way meant to ridicule your question. Teachers have students explore this question for themselves empirically rather than suggesting they take any result on faith by providing things like lids and wire. Large lids work best.

I think Nadav has addressed the calculation issues and geometric issues below and where the first error entered.
• #### Carl Dalton

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Quote: You assume a square of that perimeter will encompass a circle of that perimeter, and go from there. The base assumption is incorrect.

No: You assume the I assume, just as the sciences base their theories on assumptions rather than empirical facts.. The diameter of the 120 cm circle is exactly the same length as the four sides of the square; therefore the four points where the circle and the four lines of the square meet & merge is "empirically" shared spatially,

Quote: As far as I'm aware, Pi was originally measured and proven empirically,

No it has not. If Pi had been empirically "measured" it would not be an "Approximation" "Approximate to" "Approximately Three Diameter Lengths".

The 22 over the 7 in the improper fraction of Pi or 3 diameters and 1/7th of a diameter length; represents the circumference of the circle; however as explained in the further clarification post, using the yellow square card to define the three separate areas of the circle, the line, and the remainder of the square; it was and is physically impossible for Archimedes or any one else to physically measure a circles length.

A circle can be divided into 22 "mirror image" equal parts; 7 equal parts; any number of equal parts; but a circle given arbitrarily 22 equal parts; and then divided by 7 is not a circle being divided by 7;

But rather the number 22 being divided by 7 = 3 pseudo diameters, and an "Irrational" = "Unmeasurable Bit" of •14285714285 "∞" because it has no Ratio".

In conclusion: I have provided 4 methods that serve to define the length of a circle and the area; and all four methods provide exactly the same answer; And given that it was the Sumerians Mathematicians who were the originators of the geometry used by both the Egyptians and the Greeks; And they and their Astrologers who were the devisers of clocks, and 360 degree circle 3, 500 years ago; remember the old adage "Beware Greeks Bearing Gifts"

Disprove the arithmetic. if not its proven

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Feb 22 2014: I'd have gladly disproved the simple arithmetic if it was in proper mathematical writing. Translating paragraphs is hard enough when they're describing simple arithmetic, never mind geometry without the proper drawings alongside it.

Either way, I found the problem. Its still in the same quote:
"Giving 360cm to the 360 degree circumferential length of the circle; which is ¾ quarters the length of its squares 480cm perimeter; and each degree of the circle is 1cm in length"

Why on earth would each degree translate to 1cm circumference length, when all I know about the circle is its diameter being 120?
You just used what you were trying to prove as part of your proof.

BTW, my previous explanation is a different way of saying the same thing. Either way, this is where the mistake is. You assumed their perimeters were 360 and 480 AND that they also touch at four points. Each assumption is fine in its own right, but you can't assume both, as they contradict (even if they didn't contradict, you still don't assume both, you're supposed to assume one and derive the other from it, to prevent exactly this type of situation where you make contradictory assumptions).

If you don't believe me, grab something circular, measure out its diameter, then use a known length of string to measure the circumference. Its not a terribly accurate method (the string stretches and never follows the perimeter exactly), but it was good enough that the ancient Greeks realized it was "three and a bit" as opposed to straight up 3.
• #### Fritzie -

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Feb 22 2014: Have you checked for real circles? Jar lids will work.
• #### Carl Dalton

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Feb 22 2014: Addendum 22 - 02 - 14

Empirical clarification:

If we take a square of yellow colored card, and then use a compass to inscribe a blue circle onto the surface area of the square card; we have in effect, divided its surface area in to three separate areas of space, the area of the yellow circle, the area of the blue line, and the area of yellow that remains of the square.

If we then ask our selves the question, what is the area of the circle exclusive of the other two areas?

It becomes obvious that we have a question that can only be answered by mathematical means; because it is impossible to both separate, and exactly measure each of the three areas, by any physical means.

However using mathematics, we are able to find the exact area of the circle, and the area remaining of the square, because we are able to both separate and limit, areas and volumes of space, without need of physically imposed boundaries.

In sum: A circle is defined by the extent of its radiated/radius limit, relative to its circumferential length; not circumferential line, or boundary.

Note: The four methods of finding the area to a circle, serve not merely to confirm that my own work is correct; but also despite the works of the Ancient Sumerian Geometers having been plagiarized, and usurped by the Greeks, the four methods serve to prove that "Theirs was also correct".

However, despite the simple arithmetic/evidence involved being self evident/incontrovertible, as to the 3-1 ratio of a circle; I am not expectant of many if any, comments either acknowledging it, or supporting it (Silence speaks volumes) for two reasons;

1. It is virtually if not totally impossible, to overcome a belief, that is more than 2000 years old