Xah 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
slight update Cornu Spiral.
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. 〔►see 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?)
hoping to read this book:
- A Course In Universal Algebra by Stanley N Burris, H P Sankappanavar. @ http://www.math.uwaterloo.ca/~snburris/htdocs/ualg.html
but my plate is quite full already….