5 ms·
Aztec Diamond
- kmm 4y agoThere's a beautiful video by Mathologer about this subject, giving some intuition on why the outside areas are "frozen" https://www.youtube.com/watch?v=Yy7Q8IWNfHM https://www.youtube.com/watch?v=Yy7Q8IWNfHM
- joe-collins 4y agoI'd love to read a few paragraphs on the subject, but a 50 minute video to gain some insight into math trivia is out of the question.
- downboots 4y agoPlenty of reading in their video description. The intuition is one can construct larger tilings from smaller ones using a weird trick in a way that prefers frozen corners.
- ask_b123 4y agoWhy is it called Aztec though?
- kmm 4y agoAztec pyramids have a characteristic stair-stepped design, which when viewed from atop probably looks reminiscent of a tiling. A similar story probably applies to Aztec Codes https://en.wikipedia.org/wiki/Aztec_Code https://en.wikipedia.org/wiki/Aztec_Code
- School-Cotton 4y agoThat's true of all or most Mesoamerican pyramids as far as I know, not just Aztec ones. (Mayan, Teotihuacano, etc.) I suppose the Aztecs are the most famous Mesoamerican group in the popular imagination, though.
- thaumasiotes 4y ago> I suppose the Aztecs are the most famous Mesoamerican group in the popular imagination, though. Maybe, but they're not famous for pyramids. I would always say Maya if the prompt was American pyramids.
- monetus 4y agoThere is a map in counterstrike named Aztec with a stepped pyramid. I always think of mortarless marvels like macchu Picchu when I think of Mayan architecture. - just an anecdote
- thaumasiotes 4y agoBut Machu Picchu is an Inca city. Here's a Maya city: https://en.wikipedia.org/wiki/Chichen_Itza https://en.wikipedia.org/wiki/Chichen_Itza
- monetus 4y agoThis is true, and thanks for reminding me about chichen itza, but I just wanted to emphasize how blurry the cultural lines are to the people around me - at least where I am in the Appalachias. My city has Mayans with Mayan restaurants. Not too long ago though, a kid told me he had thought the Mayans all died out, like the Romans he said. Sorry, this is all kinda tangential. That kind of blurriness is something I'm super interested in.
- School-Cotton 4y agoYeah, it seems to be a relatively common (false) belief that the Mayans died out or even mysteriously disappeared. In reality their “classical” civilization declined and was eventually completely conquered by Spain, but as you point out, the people are still around. There are still millions of ethnic Mayans, who still speak Mayan languages, primarily in Guatemala and to a lesser extent in Mexico. The Incas were separated from the Mayans by thousands of miles of jungle (and their civilization reached its height hundreds of years after the Mayan decline). It’s unlikely they had much direct contact, if any. For what it’s worth the Romans didn’t die out either, again their civilization declined but their cultural and biological descendants are alive and well in the form of Italians, Spaniards, etc.
- mathandstuff 4y agoI wrote some open source code a few years ago that introduces a simple way to convert LU factorizations into a Determinantal Point Process sampler and used large Aztec diamonds as the example https://gitlab.com/hodge_star/catamari https://gitlab.com/hodge_star/catamari
- sherpal 4y agoIf people are interested in playing with those, I made a website a while ago where you can generate Aztec Diamond (and other shapes): https://sites.uclouvain.be/aztecdiamond/ https://sites.uclouvain.be/aztecdiamond/
- deleted 4y ago[deleted]
- hwc 4y agoMy contribution: https://halcanary.org/mathapplets/toadshuffle/#64 https://halcanary.org/mathapplets/toadshuffle/#64