Maths History with Maths Cat

i love having a brain and desmos and a skewed sense of humor

The Ulam Spiral

If you draw numbers on a grid, starting from the middle, in a spiral pattern, like so:

and then mark the prime numbers:

you'll notice they form distinct diagonal lines on the grid.

Via Wolfram:

Unexpected patterns of diagonal lines are apparent in such a plot. This construction was first made by Polish-American mathematician Stanislaw Ulam (1909-1986) in 1963 while doodling during a boring talk at a scientific meeting. While drawing a grid of lines, he decided to number the intersections according to a spiral pattern, and then began circling the numbers in the spiral that were primes. Surprisingly, the circled primes appeared to fall along a number of diagonal straight lines or, in Ulam's slightly more formal prose, it "appears to exhibit a strongly nonrandom appearance" (Stein et al. 1964).

The compound of ten triangular prisms is a chiral uniform polyhedral compound. It has 50 faces (20 triangles, 30 squares), 90 edges, and 60 vertices.

In the song The Twelve days of Christmas, your true love gives you a bunch of gifts throughout the twelve days. Assuming that each day they give you a new gift (that being the partridge in the first day is not the partridge in the second day), you will receive a total of

12 Partridges in pear trees

22 Turtle doves

30 French hens

36 Calling birds

40 ~Golden Ringss~

42 Geese a laying

42 Swans a swimming

40 Maids a milking

36 Ladies dancing

30 Lords a leaping

22 Pipers piping

12 Drummers drumming

That is a total of 364 gifts. That is a lot of gifts.

Which is more than 50% of all the items.