Nice. Would three of these fit together to make an equilateral triangle?

Numbers 0-2025 in a grid in permuted order.

And since 2026 = 2·1013 is a semiprime, multiplying mod 2026 by any odd number not a multiple of 1013 gives a permutation of 0-2025:

The numbers 0-2025 in base 45 arranged in a grid.

An alternative view, showing the numbers 0-2025 (in base 45) arranged nicely in the grid:

A grid of 2026 coloured boxes.

2026 = 45²+1 which is exactly the number of coloured boxes in this image - and there are exactly 45 of each type of box, except the empty red box on the top left,which is unique. See oeis.org/A002522 for more details.

Impressive. Might have to get myself a 5 for Christmas!

Nice! What is the screen resolution? I tried some Shadertoys on a Pi 2 a while back - worked nicely, but so slow (this was with an HD screen).

The n = 0 case works nicely here too - take a 1x1 grid, black out the single square, the remaining 0 squares can be tiled with 0 trominos.

How about the n = 0 case? The product of 0 functions is constant 1 whose derivative is the sum of 0 values, which is 0. Taking 0 and 1 for the sum and product of the empty set is exactly what is needed to make this sort of trivial base case work out.

Street sign for Polygon Road

Courtesy of diamondgeezer.blogspot.com/2024/02/poly...

Look at the red dots, one 9x9 square, then 16 rectangles that pair up to make another 8 9x9 squares, make 9³ altogether.

Here's a picture:

Heron's Theorem

A nice variation on the traditional proof of Heron's formula. Given triangle ABC with incentre I, construct IG perpendicular to BI & complete the diagram as shown. Similar triangles show that LG = βγ/r and Euclid I.43 does the rest:

SSEC Scene in Walk East on Beacon YouTube video by Anne Pasek

Great! Mentions the SSEC, which I'd never come across, excellent film extract here: www.youtube.com/watch?v=eKkn...

2025 dots arranged to show that 2025 = 1³+2³+3³+4³+5³+6³+7³+8³+9³ = (1+2+3+4+5+6+7+8+9)²

A nice visual demonstration that 2025 = 45² = (1+2+3+4+5+6+7+8+9)² = 1³+2³+3³+4³+5³+6³+7³+8³+9³: