Trigonometry without a word
Two arctangent identities, seen through a geometric proof without words.
geometrytrigonometry
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Problems to solve and ideas to explore.
Stirling’s approximation, but weaker
Compare factorial and exponential growth by proving a limit.
analysissequences
Simple but fun
A permutation of an odd-sized set produces an even product. Can you see why?
number theoryparity
Hilbert matrices
A deceptively simple matrix: can you prove it is always nonsingular?
linear algebraanalysis
Conservative polynomials
What happens to a polynomial when we take its absolute value?
algebrapolynomials