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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.

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  • 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.
    • 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
      • 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.
        • 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?
  • 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.
    • 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.
      • 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.
        • 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
        • 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
  • 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.
    • 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
  • 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.
  • 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
  • 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
  • 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.
  • 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
  • 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.

    YOUR PROBLEM NOT MINE

    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.
    • 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
  • 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!
  • Mar 20 2014: You have just defined yourself

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

      With Pi you get exactly the same result
  • 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
  • Mar 1 2014: Bryan Maloney

    Stop wasting your air space, your not even amusing,
  • 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
  • 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
  • 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.
  • 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
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      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.
      • 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.
  • 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

    Addendum

    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.
  • 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.
    • 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
      if we have to read your long and bad expressed posts
      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
      • 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
  • 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
    • 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.
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    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.
    • 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
      • thumb
        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.
        • 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.
    • 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
  • 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.
    • 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.