Today, March 14, is Pi Day, because the date can be written 3/14 which is the first three digits of pi.
The mathematical constant of pi is the ratio of any circle’s circumference to its diameter.
Expressed in decimal notation, pi is 3.14159…(there’s your number for the day) and continues on forever without ending and without repeating because the ratio is an irrational number.
I understand pi, but I’ve never understood it.
With the all the symmetry that Nature and Numbers provide, I’ve never understood why a simple ratio of a circle’s diameter to its circumference should not be a simple number.
I’ve also found it fascinating that for any two integers next to each other on the number line (i.e., 3 and 4, 6 and 7, 10 and 11), the sum of those two numbers is difference between their squares. For example, if you pick 2 and 3, their sum is 5 and the difference between their squares (4 and 9) is 5 also.
a + (a + 1) = (a + 1)2 – a2 is a beautiful equation.
Since there is so much symmetry in Nature and Numbers, why must a simple ratio be irrational? It would seem to make more sense that the circumference of a circle is exactly 3 times its diameter.
As I have scads of free time to ponder silly stuff like this, I have hit upon a possible answer that is sadly untestable.
Could it be that the expanding Universe is to blame for the extra .1415926535897932384626433etc that is tacked on to the ratio?
I hope I can explain this well.
Imagine the known Universe shrunk down one dimension and that everything that was, is, and will be exists on the skin of a balloon. The skin is a plane which is two-dimensional as the inhabitants can only move in the x and y directions. The balloon itself is expanding into the third dimension.
Due to this expansion, and its correlating acceleration, through this extra dimension, perhaps there is some distortion going on in the geometry of a circle. In a static Universe, perhaps the ratio of the diameter to the circumference for a circle is indeed 3. However, the expansion and movement through the third dimension causes a distortion in the time-space fabric that stretches out the circle ever so slightly that gives the ratio that extra .1415926535897andsoonandsoon.
Inhabitants of the expanding Universe see the circle as perfectly round and don’t notice the distortion because they are in the same frame of reference as the circle and so as the circle is distorted, so are the denizens of the balloon Universe.
Perhaps it is the same way with us on our three-dimension balloon moving through the extra dimension.
Like I said before, I have no way to prove this, but it’s thoughts like these that have my mind running around in circles.
Happy Pi Day!