Xah's Math Blog Archive 2011-12 to 2012-04

update, with video: Grigori Perelman: Will You Decline 1 Million to Make a Statement? 📺

minor updated. Buy the book: “Curves And Their Properties” by Robert Yates


updated. Geometry: Transformation of the Plane


slight update Cornu Spiral.

Math Font, Unicode, Gothic Letters, Double Struck, 𝔄 𝔅 ℭ

Why Does π Occur All Over Math?

for example, just about every interesting plain curve involves π. See: Visual Dictionary of Special Plane Curves.

the only reason i can think of is that it's the circular function. (that is, the essence of trig function. 〔➤ Sine Curve〕)

but it happens in probability too. For example: Buffon's needle.

the Wikipedia article indicates that Buffon's needle is part of a problem in geometric probability. So, perhaps that ties to the circle, therefore π. Circle itself can be considered as a result of circular function. i.e. the trace of a constant length with one end fixed and the other end moves at a constant speed. So, we can consider that the relation of Buffon's Needle is tied to circular function.

but are there other occurrence of π that has little to do with circle? (For example, it appears in series often. How's this explained?)

Kawai MP9000 piano dodecahedron
Magic Polyhedrons
Conway's Game of Life within Conway's Game of Life. Video made by Mike Stay (aka metawetayt on YouTube.)

Conway's Game of Life Recursively Defined

zonohedron krishna by Russell Towle
A zonohedron by Russell Towle.

Russell Towle Died (1949 to 2008)

hoping to read this book:

but my plate is quite full already….

Xah Lee Introduces Stanford University Courses

Review of Khan Academy by Xah Lee