No. 3.1415926535897932384626433832
Well, now we get to the number I love the most. I think this number bespeaks a glory of the heavens in such a way that words will not suffice, but alas, I must publish. Two disclaimers: to all those who know me, I am not trying to show off, but rather to share something beautiful to me; and to those who I do not know, this may seem to be rather parochial, or pseudo-mathematical, but I firmly believe in it, and the patterns that follow are evidence enough for me to denote intelligence behind nature.
We all love circles. They represent wholeness, completeness. We speak of life coming full circle for us. We even say, “the circle of life”. Well, circles are astounding mathematically because of a certain number which is irrational, that is, can not be expressed as a fraction of integers. However, that number can be expressed as a ratio:
that is, pi is the ratio between the circumference of a circle and its diameter. Simple enough, except that since the number is irrational mathematically speaking, one can know only either the circumference of a circle exactly or its diameter exactly, not both at the same time exactly.
Pi comes into play with another aspect of circles. The area within a circle is measured as such (“A” means area, “r” means radius):
So we see that pi relates to both the circumference, radius, diameter, and area of a circle! What about a circle’s 3-dimensional counterpart, a sphere, one of the most beautiful shapes, in my opinion, also the most compact of shapes? It turns out that to find the volume of a sphere one has to look no further than the astounding pi (“V” means volume) :
It does seem amazing that this irrational number has such an intimate bond with circular objects. And although this math is rather basic, when one really ponders it for a while, one can see beauty in it. But let’s move on, shall we.
Pi, though an irrational number, which again is a number that can not be expressed as a fraction of integers, can actually be expressed as a sum of fractions! I’ll give the beautiful, compact equation first and then explain it after:
That looks Greek to me! Indeed there are two Greek symbols contained in that equation. For those that are not mathematically inclined, the equation is really not as scary as it looks. The sideward “8” symbolizes infinity, and the large “E” looking character is the Greek letter Sigma and denotes a sum, namely the sum of the fraction [(-1)^n]/2n+1, where the value of each successive iteration of the fraction changes as the value of “n” increases from 0 to infinity. It looks like this:
Do you see a pattern developing? It seems that pi has both an intimate relationship with the circle, and an intimate relationship with the alternating positive and negative inverse of the odd natural numbers. Interesting, isn’t it?
Again, I know this may seem pseudo-mathematical, but to me this is beautiful, and bespeaks of an intelligent being uniting numbers with the most perfect of shapes.
Thanks for reading!!!
outoftheloveofpi 