Puzzle Description:

A (relatively) simple way to visualize the basic trigonometric subtraction/addition identities. In this case there is a 9-12-15 triangle and a 12-16-20 triangle. They combine to make, roughly, a 7-24-25 triangle. As much as I'd like to use more complex numbers, it would make the image too big. Also I kept getting alternate solutions until I made the lines a bit thick. Another way I remember figuring the formulas was to, say, set x=y or x=0 and then I could figure match up which sin/cos products went with which. I'm not sure how I learned it in high school. My teacher was very good, but I had to memorize the formulas. But I was pleased to find a diagram like this when I googled years later.

#1: Web Paint-By-Number Robot (webpbn) on Apr 10, 2022

Found to be solvable with moderate lookahead by blurglecruncheon.

I found two places that needed lookahead: the bottom 8x4 corner and R6-10 C7-22.

For the lower right there are lots of ways to do things, but note R27/28 must both have green dots in C33/35 or else you would have 1/2 in one row and 2 in the next, this making a 2 in some column.

For the upper bit you can work on row 6 with edge logic and some 2-way logic, or you can work on column 7. If a green is in C7R6, then wherever you place the 2 in C10 puts a 2 in C11. Otherwise, you get 2-way logic or zigzag lines that run into the edge of the remaining unfilled square.

All this maths hurts my head!

When I was on the math team, we would draw a circle with 30-45-60-90-120-135-150-180-210-225-240-270-285-300-315-330 and 360 degrees marked (in 12ths and in 4ths), and write in the sin and cos of each degree measure. We would draw these daily, and see how fast we could make them, so that they'd be burned into our memories.

Wow.

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