In an earlier post Spaghetti Loops, we asked several problems that we promised had something to do with the number e.
The first question really has to do more with the famous harmonic series; in this post we showed that the sum
1 + 1/2 + 1/3 + 1/4 + …. + 1/n
adds up to about the natural log of n, plus a small constant, Euler’s γ ≈ .577215664901… In other words, to sum up to, say N, at least e(N- γ) terms are used.
The topology of paper doll folding patterns explains geometrical symmetries, as Chaim explains in this short video:
(And much more deeply in The Symmetries of Things.)
The video was produced by Research Frontiers, at the University of Arkansas
Just why does e appear in so many guises?
We settle some business and address the game of Plinko.
We discuss math on TV, the smallest ungoogleable number and a devilish game with billiard balls.
Karl Schaffer of Math Dance shows us some geometry tricks!
We answer last weeks puzzle, discuss the law of small numbers and ask again what is the smallest positive counting number that Google can’t find?
We visit the Fayetteville Farmer’s Market, soliciting math questions, and pose a problem about funny walks.
We conclude our interview with Dana Richards, editor of Martin Gardner’s Colossal Book of Short Puzzles and Problems pondering how to cut a hole through a cube large enough that another, same-sized cube can pass through!
That the worm falls off the end of the rope depends on the fact that the incredible
harmonic series
1 + 1/2 + 1/3 + 1/4 + . . .
diverges to infinity, growing as large as you please!
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