Arrangement of 1-2-root(5) triangles.
Inspired by mathani’s cool picture. This was done while investigating in GeoGebra.
Questions this prompts: why does this only work for these triangles? Why is the bottom right arrangement a square? Where do those blue triangles go off to? Does it involve coffee?
The laws of nature are but the mathematical thoughts of God. - Euclid
Saw these mathy anagrams at the Futility Closet today. Needed to animate them. I used GeoGebra after not finding an easy web app to do it, and just used several functions that had f(0)=0 and f(1)=1 to muddle up the letter progress. Can you guess any of the functions from the animation?
The 2014 Bridges conference on Arts and Mathematics is starting tomorrow (August 14th) in Seoul. These three works of mine will be on display in the art exhibition. More information and links here:
Such a prescient and important read: How We Think — John Dewey on cultivating the art of reflection and fruitful curiosity in an age of instant opinions and information overload.
This sketch has a section of an Archimedean tiling (rhombitrihexagonal) and its dual.
The dual is found by taking the center of each polygon, then connecting those as vertices if the polygons they’re in are adjacent (share an edge).
When you move the slider or hit the play button, the sketch will shift between the original and the dual.
It’s called the dual, because if you do that again, you get back to the original (or a variation of the original.) You can use this technique to find the structure of tessellations.
If you download it, this sketch has tools to make your own. One tool finds the center of a polygon (barycenter), and the other family of tools is for making the animated dilations.
Inspired by bmk sketches like at [url]http://geogebrart.weebly.com/blog/duality-2[/url]
Sketch at GeoGebraTube.