This puzzle consists of four hinged pieces which can be folded one way to a square and the other way to an equilateral triangle. Master puzzler Henry Dudeney demonstrated a wooden model before the London Royal Society in 1905.

The digits of π, translated into music.

The video also shows some fun facts about π.

Combinatorics. Combinatorics began as a formalized treatment of efficient ways of counting certain collections of objects which arise relatively often. Nowadays the word ‘combinatorics’ can be used to refer to pretty much all of finite mathematics, and the original field is more specifically called “enumerative combinatorics”.

The things in parentheses are not fractions (they don’t have a fraction bar). These are calledbinomial coefficientsand (n [over] k) represents the number of ways to choose k balls from a set of n balls. Pascal’s triangle is an arrangement of these numbers where (n [over] k) is the k-th number in the n-th row; it is very famous to be a useful way of visualizing many of the properties of the binomial coefficients.I’m experimenting a little with how to display the theorem statements. Not really sure what I like yet.

The proof of Sum of Square Numbers!

This is NOT a proof, but it’s still very beautiful and good for intuition.

### "That’s not what I got."

### "You missed a minus sign"

Great article by Evelyn Lamb on one of the

otheruses of pi: as the prime counting function.

See the use of phi as the totative-counting (totient) function. Lord, number theorists love to jeopardize notation. Also, Is it just me or does the graph of the prime counting function look oddly like the stable isotope curve? Gosh, that’s cool. [CJH]