Happy Pi Day!

π is my most favorite number. And today is March 14th (3.14), celebrated as the Pi Day among math-lovers. Here are two reasons why this mysterious number fascinates me:

First, it is an irrational number, which means that it can not be expressed as a ratio of two integers. Take any two integers, however big, but you can’t get the exact value of π by taking their ratio. The decimal points in π don’t follow any pattern and it never ends!

And second, it is also a transcendental number, which implies that no finite sequence of algebraic operations on integers (roots, sums, etc.) can be equal to its value. [From Wikipedia]

It really amazes me how a mathematical constant, very commonly found in nature (it’s the ratio of a circle’s circumference to its diameter), has infinite, pattern-less decimal points.

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For Sudoku fans out there, here’s a Pi Day puzzle:

Rules: This pie has 12 wedges.  Fill in the grid so that the numbers 1-12 appear exactly once in each region of the pie.  There are three types of regions in this pie, each containing 12 cells.  They are: each of the six rings going all the way around the pie; each of the six pairs of opposite wedges; and each of the six adjacent pairs of wedges of the same color. Here’s a PDF file. [Hat Tip: 360]

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