I was intrigued by the muted color palette. You simply used 0.8 for v instead of 1, and it makes a nice difference.

Because you can backtrack, I used symmetry: There are 4*3 = 12 ways from Y to a K. 12^2=144.

I figured it was like taking pictures of the Aurora with your phone. You can barely see some color in the sky, but the phone shows it much brighter.

30-60-90 right triangle. Inscribed angle is 30/2 = 15.

Rhombus. Area ratio is 2:1

Interesting result. Tucking it away for later in geometry. Then again, how often do you start with the premise of angles in arithmetic progression?

I know all the digits of pi: in decimal they are 0,1,2,3,4,5,6,7,8,9 (there are some repeats).

So people were wrong in calling her 'uniquely' unqualified.

cheerleader
so and so
what’s her face
the ugly one

Same. I've never seen it in writing before.

Wu-Tang is for the Giants.

Usually, these things from XKCD are either a mixture of real and made-up. In this case, I feel like they're either all real or all made up, but I can't decide which.

This is soooooo embarrassing.

Sometimes it's easier to get directly to the answer 9*(2nd eq.) - 8*(1st eq.) = 10x+9 = 9*19 - 8*13 = 67. Not an easy mental math, so I don't think that's easier in this case.

Sorry typo. sqrt(23) as it is in the Desmos.

The key insight was the line has distances in the ratio 1:2:3 from the three centers.

Desmos | 3D Graphing Calculator

Nice. The line sought is 2x+3y=-6. The two planes are 2x+3y+/-sqrt(26)z=-6 www.desmos.com/3d/k4oxuldkj8

I like the special right triangle windows. I wonder if it would be worth making ones with period/amplitude changes. Also, it looks like you made a cosine grapher as well!

Permutations today: 52! is 8x10^67. The 7th graders lost it.

I remember figuring this rule out on my own back in high school, where to solve a problem, I needed to know which numbers have an odd number of factors.

Thanks for sharing. I was bracing for a challenge, but everything is right there.

So sweet. We had a kitty named Huckleberry who looked a lot this yours many years ago. I'll try and find a photo.

I like math now.

I'd like to say I did that, but I doubled the 27 three times. When I got 216 I realized that would have been easier.

Some "let them eat cake" energy going on there

It's funny because it's true.
(Or the least untrue things he's posted.)

I don't think your argument is sound. There's no guarantee that for any P the triangular cross-section can be adjusted by epsilon and intersect all six sides. On a cube-like shape it does, but for my shape it sometimes can't. Does every F=6, V=8 shape have some P that does work?

Desmos | 3D Graphing Calculator

Looks like you can get a hexagon. At least for this simple case. www.desmos.com/3d/brrufqrvj4

No. A tetrahedron with the tips of two corners sliced off fits the description. I'm having trouble picturing whether it has a hexagonal cross-section.

You guessed correctly. I don't have that one, just the ones that skip by constant amounts.