Alex

I do maths for fun, and sometimes make puzzles and games. he/him.

[Alex @zithral]

@geogebra @cs_kaplan Here's a few quick designs.

[Alex @zithral]

I've been using @geogebra to play around with edge designs for @cs_kaplan's Spectre tiles.
https://t.co/LW1zdEbWIw

[Alex @zithral]

I have ~250 lasercut Tile(1,1)/spectre tiles. I think I need more.
Thanks @chenonetta for cutting these for me!

[Alex @zithral]

Looks like someone beat me to it:
https://t.co/emyQnkJ1p8

[Vincent Pantal🍩ni @panlepan]

Exploring the #Spectre tiling with @MathigonOrg is just perfect. You can group tiles, rotate them, snap them together.
https://t.co/hGrPCKlspw
Cc @cs_kaplan @divbyzero

[Alex @zithral]

I made a simple @MathigonOrg Polypad for playing around with @cs_kaplan's new #Spectre tile:
https://t.co/bqsuPLKBBP

[Chenonetta @chenonetta]

So @zithral asked if it would be possible to laser cut a stack of sticky notes... and the answer is well uh, sort of? We only got a little bit of fire...

[Alex @zithral]

Aperiodic monotile that tiles without reflections!

[Alex @zithral]

We could go further, and have 100 triangular pieces, and try to group them into 10-iamonds of the same shape. Might be possible?
If this approach is impossible, it could still be possible to divide the cake into five pieces that aren't polyiamonds.

[Alex @zithral]

I have a cake in the shape of an equilateral triangle, and want to cut it into pieces that are all the same shape. What are some different ways I could do this?

[Alex @zithral]

We spent a while trying to divide the cake into 5 pieces. Our approach: divide it into 25 triangular pieces, then try to group those pieces into five of the same pentiamond. We're pretty sure that's impossible.

[Alex @zithral]

@JamesPicone Yep, I left that intentionally ambiguous :P
I'm interested in the same-size case, but the other case is also very interesting.

[Alex @zithral]

The values I settled on were:
0dB = 1
1dB ~= 1.25
2dB ~= 1.6
3dB ~= 2
4dB ~= 2.5
5dB = sqrt(10) ~= see puzzle in previous tweet
6dB ~= 4
7dB ~= 5
8dB ~= 6.25
9dB ~= 8
10dB = 10

[Alex @zithral]

Find integers x and y such that:
1.25^x * 1.28^y = 10

[Alex @zithral]

Recently I've been working with PSNR values, which are measured in decibels (unfortunately). I wanted some nice round numbers that are approximately +1dB, +2dB, +3dB, etc.

[Alex @zithral]

@DavidKButlerUoA "David Butler enjoyed producing 5" was enough of a hint for me to work it out too, thanks :)

[Alex @zithral]

At #100factorial today we worked on a Skyscrapers puzzle, using video cassettes to represent the buildings.

[Alex @zithral]

Got another colour :)

[Alex @zithral]

I got some lasercut aperiodic monotiles! Both hat and turtle polykites.

[Alex @zithral]

@DavidKButlerUoA , I'll bring these to #100factorial this week!

[Alex @zithral]

Can we find the turtle polykite in real life? This is the closest I've found so far.

[Alex @zithral]

Is it just me, or does this lake look kinda like the new "hat" aperiodic monotile?
https://t.co/99xzV7KPuS

[Alex @zithral]

So close! (Okay, maybe not.)