Saw this great image at Peano’s from Elijah Porter, (see his Flickr for much more mathart) and had to play around with it.
I love reptiling. So this GeoGebra sketch has a tool that divides up any quadrilateral in the trapezoid reptile pattern. Have fun! (At GeoGebraTube.)
A dynamisized version of Euclid’s proof of the Pythagorean Theorem. Steps, but you can still change the triangle to any right triangle.
At the ‘tube: http://www.geogebratube.org/material/show/id/38900
So what do you think about “dynamisized”? Dynamicized? Dynamicalled?
Today’s Geometry Daily (#425) made me realize that adjacent similar rectangles have a pretty nice relationship. All the differently colored rectangles in my diagram are similar. (There’s a tool in the sketch that helps draw them.) Isn’t that cool? It’s not too hard to understand once you notice it. The arrangement holds for any proportion rectangle.
GeoGebra sketch at the ‘Tube: download or java applet. (The mobile-ready applet doesn’t have the similarity tool, but everything else works.)
I was inspired by this #mathart: http://mathhombre.tumblr.com/post/48437097612/love-these-planar-patterns-inspirational
It’s by Daniele De Nigris, who has a lot of geometric art: http://www.flickr.com/photos/denigrisdaniele/sets/
It got me thinking about showing tessellations by a wallpaper group type approach. Instead of modifying the edges, modify a pattern in the tile, and then the motions will be shown by the way the patterns connect.
Technical info on the wallpaper groups: http://en.wikipedia.org/wiki/Wallpaper_group
In this tiling I was experimenting with tangent circles for the lines.
GeoGebraTube: download or mobile-ready applet
EDIT: Danny Brown, @dannytybrown shared his tessellation booklet (docx), which has a good wallpaper section. It’s among a lot of materials he’s shared at: http://www.gfsmaths.com/the-book.html
Came across this great book designer’s page http://retinart.net/graphic-design/secret-law-of-page-harmony/ via ilovecharts on Tumblr. It’s enthusiastic, detailed, lots of eye-popping illustrations. It’s about the best place to put content on a page.
Not only is there an excellent geometric method for producing this best text layout - for any proportion page - there’s a bevy of geometric claims about the result.
I thought it was fun, and started just because I wanted to see the layout for different shaped books. I’m a little too pleased with how it came out. Hope you like it.
It’s on GGBtube for download or mobile applet.
Craig Winske made a nice sketch showing the mean dynamically and wanted some helping adding the median. Here’s his blogpost about it. I did that and a little guessing game, built on his nice structure.
Saw this beautiful rug at Islam and Art, and wanted to think about the tessellation. But one of the things I like about it is the inferred motion, so I tried to animate it, too. It’s a little clunky in GeoGebra because sooo many points are animated, but I’m pretty happy with the gif. Interestingly it’s smoother in the mobile (HTML5) version.
On GeoGebraTube, of course, so you can make you’re own. For download or mobile-ready applet.
Geeky GeoGebra tidbit: I make the checkboxes affect each other using the SetValue command in the Scripting - On Update panel. Like SetValue[o,False] (or SetValue[α, 0°], or …) but this is the first sketch where I used a conditional. So If[!(o||s_1),SetValue[u_1,True]] turns on the u_1 textbook if both o and s_1 are off.
A very cool dissection puzzle from Cut the Knot, made into an interactive puzzle with GeoGebra. Alexander noted in the comments and on his site that the puzzle is from Daniel Hardisky.
This GeoGebra sketch is to let students experiment with best paths when travel speed varies. It was inspired by this tumblr post on ants being able to find the best path, and it’s also reminiscent of Tim Pennings’ dog Elvis who could “do calculus.” (pdf) The general idea is know as Fermat’s Principle.
On GeoGebraTube for download or mobile applet.
Thought today’s Geometry Daily was fascinating. Are the parallelograms similar? What’s the scale? Is it fractal? How would you construct it? Does it generalize?
So onto GeoGebra! Here’s the sketch for download or applet. (Works surprisingly well in HTML5.) It can be a little sluggish, because there’s a lot of detail.
