Birkhoff's Theorem on the determination of doubly stochastic matrices. #math #algebra #probability

Plotting a function with a lot of local minima

johndcook.com/blog/2023/06/1…

In the Star Trek universe, warp factor w corresponds to a speed of w^3 c.

So for example, warp 2 is 8 times the speed of light.

Primality certificates johndcook.com/blog/2023/01/0…

Balanced tournament designs

johndcook.com/blog/2022/09/1…

'I've decided that the Yoneda lemma is the hardest trivial thing in mathematics.' -- @[email protected]

Digital signatures with oil and vinegar

johndcook.com/blog/2019/03/1…

Discrete Fourier Transform (DFT) over a ring: en.wikipedia.org/wiki/Discrete_…

40585 = 4! + 0! + 5! + 8! + 5!. The only other numbers like this are 1, 2, and 145.

Galileo's theorem: The area of a circle is a mean proportional between the areas of any two similar polygons, one of which is circumscribed about the circle and the other is isoparametric with the circle.

Area of a quadrilateral as a determinant

johndcook.com/blog/2024/02/2…

The sum of the reciprocals of consecutive integers is never an integer. johndcook.com/blog/2021/01/2…

Visualizing a determinant identity

johndcook.com/blog/2023/07/1…

An elliptic curve can have only a finite number of points with integer coordinates.

pick any number, and write it in Chinese numerals. count the number of strokes to get a new number. repeat to get a sequence of numbers-
you will always end up looping at 2 二, or at 3 三, or back and forth between 4 四 and 5 五. (Or you picked 1一.)
pictured is 1 up to 100

Hilbert-Waring theorem en.wikipedia.org/wiki/Waring%27…

12345678910987654321 is prime.