TED Conversations

This conversation is closed.

Piece of cake

PI isnt really an infinite quanity.PI is a circular boundary in a two dimensional plane.Very limited within still more limits.

If you were to draw a cirlce and have a 4 year old child trace their finger around the perimeter until they came to the end and got them started it does not take long before they exclaim-there is no end.

This is the type of insght a super computer cannot master yet.It follows the instrucion to find the end of a continuos line endlessly and never reaches a conclusion.

The vexing question I have is whether or not the PI ratio and its infinite non repeating digit quality hold significance outside of the boundary of circular two dimension plane.A commutation of its infinite ratio property outside of its border and dimensional boundaries if you will.

Is there a quick shortcut to what Im looking for on this one?The 4 year couldnt help and neither could the computer.

Share:
  • thumb
    Sep 18 2012: A guy for Mississippi explained this to me:

    PI are round and cornbread are square.

    Kinda sums it up .... Bob.
  • Sep 17 2012: e^(pi i) = -1

    If you are looking for the significance of pi, this equation might be of interest to you. This link provides a mathematical explanation: http://www.math.toronto.edu/mathnet/questionCorner/epii.html

    The number e was developed completely independently of the value of pi. I think this relationship must have come as a big surprise to whoever first discovered it.

    ------------------------------
    Addition: This equation is known as Euler's Identity:

    " http://en.wikipedia.org/wiki/Euler's_identity "
    • Sep 18 2012: Euler's identity says that e^(xi) is the same as cos(x)+isin(x) (which is evident when you see their derivatives behave the same way) and of course cos(x)+isin(x) is nothing more than a representation of a point x on a circle (where one of the axes is mutliplied by i, to make it the complex unit circle), making it not very surprising that plugging in x=pi gives a special answer. It's still a beautiful formula though.
    • Sep 19 2012: Personally I dont see the beauty in it but I may not fully understand it.

      How about a circle of one dimension with a particle inside...

      http://en.wikipedia.org/wiki/Particle_in_a_ring
    • Sep 19 2012: If all the money in the world was equal to M then

      M+infinity=infinity

      Unless its Canadian money :)
  • thumb
    Sep 17 2012: To me it seems that this is one of the POINTs where physics meets phylosophy.
    I could be wrong but is the answer to your question related to posible orientations of an object?(squared to meet three dimentions)
    A computer could be given a set of rules to be able to compute whether or not to trace beyond the point of origin and or accept ROUNDing error to preform as a young human would.(ML)
  • thumb
    Sep 17 2012: As John writes, the fact that an attempt at a decimal representation requires an infinite, non-repeating string does not make pi infinite. It is very finite. It simply is not a "rational number."

    The example John describes below is of a rational number. In his example, one- third is clearly not infinite and yet its decimal representation involves an infinite string of digits.
  • Sep 17 2012: "The vexing question I have is whether or not the PI ratio and its infinite non repeating digit quality hold significance outside of the boundary of circular two dimension plane.A commutation of its infinite ratio property outside of its border and dimensional boundaries if you will."

    I have a bachelor in physics and all the uses of pi I've come across are ultimately derived from representing some element of the problem as part of a 2D circle, so I'd say no, pi doesn't have any significance beyond circles.

    Numbers like pi don't really bother me, both the radius and circumference of a circle are normal numbers, it's just their ratio is so hard to express, the same is true for the ratio of 9 and 3 (0.33333333333333... ad infinitum). On some deeper level this has more to do with how we see numbers than with any cosmic significance.
  • Sep 18 2012: I would suggest chocolate cake with dark chocolate icing.
  • thumb
    Sep 17 2012: Quote: "This is the type of insght a super computer cannot master yet.It follows the instrucion to find the end of a continuos line endlessly and never reaches a conclusion."

    Totally off-the-wall thought, but it is not surprising to me that the super computer would face this dilema. The "instructions" the super computer are using to "solve" the problem are mathematical to begin with...a continuing series of 0's and 1's (binary code) that allow the computer to "think". Those 0's and 1's are going to go into an infinite loop themselves once they return to the starting point of "tracing around the circle".

    The difference in the 4-year old is that once the 4-year old gets back to the starting point, he may go, "Huh?" instead of just retracing the circle over and over again.

    Like you said...it's a question of insight capability.