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  • Phil Plait's Bad Astronomy: Bitesize Astronomy
    #math | The sky is 360 degrees around. But the sky has area! Area is measured in square units, like a floor area is measured in square meters. How many square degrees are there in the sky?

    Found this one via xkcd 2748. Kind of puts in context why the Moon suddenly feels so small whenever you try to take a photo.

    3 months ago | View Shared by kos
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  • The Simplest Diagram of the 17 Symmetry Types, Ever | Artlandia Blog
    #math | As a pattern junkie, you may know how to capture the structure of a repeating pattern in a diagram; that is, determine to which of the seventeen symmetry types a pattern belongs. Yes, we are talking about surface patterns, or wallpaper patterns, whose type is determined by what mathematicians call the plane (2D) symmetry groups. Turns out all pattern schematics are not made equal and, surprisingly, the most simple diagram, which is also the most useful for the non-mathematically inclined, is also the least known or, we might even be tempted to say, a well-kept secret.

    I still don't have a full intuitive understanding of all the 17 plane symmetry groups. It's relieving to see that finding the simplest schematics to illustrate each symmetry group is considered an important problem!

    3 months ago | View Shared by kos
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  • Blob Tileset
    #game-development #math | With two different types of edge and two different types of corner, we have 2^8 or 256 different tiles in a complete tileset. (...) Generally though 256 tiles is too many to produce and use. However, there is an interesting subset of 47 tiles, known as 'Blob' tiles. So called, because each tile has a central 'blob' of land or carpet, aulthough tile_0 is often depicted without for artistic reasons. These can be used to tile room, terrain or carpet areas.

    Tilesets are a big source of inspiration for me given how they can "bring to life" a simple 2D array of numbers and make it look like a "place". Combine that with a tileset editor and you can literally paint locations!

    Guy Walker's website is my favourite resource about various approaches of tiling. It is currently offline but luckily there's a mirror available courtesy of Boris the Brave.

    1 year ago | View Shared by kos
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  • Kaboom: an unusual Minesweeper
    #game-development #math #projects | Normally, the arrangement of mines is decided at the start of the game (except for some trickery so that you cannot lose on the first click). But what if there was no pre-determined arrangement, and the game was allowed to choose after you play?

    Such a creative use for a SAT solver!

    5 years ago | View Shared by kos
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  • I told you not to go for Kokushi
    #mahjong #math | We’ve all been there: you’re dealt a hand with a lot of yaochuu tiles — ones, nines, and characters — and you find yourself asking, “Do I go for the stupid thing?”

    Some probability facts for Mahjong fans!

    6 years ago | View Shared by kos
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The Simplest Diagram of the 17 Symmetry Types, Ever | Artlandia Blog

https://blog.artlandia.com/the-simplest-diagram-of-the-17-symmetry-types-ever/ Internet Archive
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#math
Date added
Oct. 2, 2024, 12:02 p.m.
Description
As a pattern junkie, you may know how to capture the structure of a repeating pattern in a diagram; that is, determine to which of the seventeen symmetry types a pattern belongs. Yes, we are talking about surface patterns, or wallpaper patterns, whose type is determined by what mathematicians call the plane (2D) symmetry groups. Turns out all pattern schematics are not made equal and, surprisingly, the most simple diagram, which is also the most useful for the non-mathematically inclined, is also the least known or, we might even be tempted to say, a well-kept secret.
Notes

I still don't have a full intuitive understanding of all the 17 plane symmetry groups. It's relieving to see that finding the simplest schematics to illustrate each symmetry group is considered an important problem!