Beautiful Geometry, by Maor and Jost
A handsome book that mixes art and math. Maor is a historian of mathematics, and Jost is an artist. Together, they fight crime. Er, no. Together, they explain and illustrate a number of geometric (and broader mathematical) ideas. These kind of math/art mashups tend to be kind of lame, but this book has a pretty good batting average of art that does a good job of communicating or exhibiting mathematical ideas. Many familiar faces, from Euclid to Fibonacci to Sierpinski. But also a number of new things to me. Like Steiner's Porism, which would take me too long in words to describe, so I will leave an enigmatic GIF:
And one different way of looking at things. We all know(?) that the stars on the US flag are arranged in alternating rows of six and five. 6 + 5 + 6 + 5 + 6 + 5 + 6 + 5 + 6 = 50.
But if you look at the field at a 45 degree angle, you can see it as a sorta triangle of the odd numbers 1 + 3 + 5 + 7 + 9 = 25 (*) stars, sitting on top of the same thing flopped over.
(Teaser PDF with a few chapters.)
(* note in passing -- the sum of the first N odd numbers is N^2.)
And one different way of looking at things. We all know(?) that the stars on the US flag are arranged in alternating rows of six and five. 6 + 5 + 6 + 5 + 6 + 5 + 6 + 5 + 6 = 50.
But if you look at the field at a 45 degree angle, you can see it as a sorta triangle of the odd numbers 1 + 3 + 5 + 7 + 9 = 25 (*) stars, sitting on top of the same thing flopped over.
(Teaser PDF with a few chapters.)
(* note in passing -- the sum of the first N odd numbers is N^2.)