(Mathhombre) Miscellanea

Triangle Divided.

There was a neat bit of mathart by someone called Delta tiling a 30-60-90 triangle rather beautifully.

Besides appreciating it, that almost always makes me want to dynamicize it. After thinking a bit, I wondered if it might make for a artsy visual way to look at triangle centers.

The buttons let you make particular shapes or centers, or you can drag the points to free explore. On GeoGebraTube.

Yin Yang Weave.

A beautiful construction from Naked Geometry. How is it made? How does it generalize?

On GGBTube for play. I think Naked Geometry found the most harmonious version. What do you think?

Color Shakes.
Used a tip from the GGB forums to colorize the different vertices’ new diagonals by putting the items in the spreadsheet instead of making them in a list. (All items in a list have to be the same color.) The color effect is by using HSV instead of RGB and indexing the Hue from 0 to 1.
Updated on GeoGebraTube, too.

Color Shakes.

Used a tip from the GGB forums to colorize the different vertices’ new diagonals by putting the items in the spreadsheet instead of making them in a list. (All items in a list have to be the same color.) The color effect is by using HSV instead of RGB and indexing the Hue from 0 to 1.

Updated on GeoGebraTube, too.

Handshakes

Warm up sketch inspired by the naked-geometry.

On geogebratube for you to play. Has a tool to make multiple copies of your own.

David Marain (@dmarain) shared an angle chasing puzzle in the 80-80-20 isosceles triangle. Quite a nice one.

I chased a bit, then modeled in GeoGebra. Then I made a tool for making an ASA triangle which was handy for making angle chasing problems. Then I generalized the problem, and found that the 80-80-20 triangle had lots of neat situations that other triangles do not. (Here it is on GGBTube)

Is there something that makes this triangle special?

P.S. Turns out Simon Gregg (@Simon_Gregg) was also intrigued by this, and made some great mathart along the way. Check out his post.

Recent GGB Work.

Two recent GeoGebra sketches had too much writing to post here. The Mario Brothers was in response to a neat post from @approxnormal (blog, GGBTube), and the complex to complex polynomial sketch was in response to Numberphile’s recent & great video on the Fundamental Theorem of Algebra (blog, GGBTube).

Bubbles.

2 dimensional patterns, translation…

Pretty?

No idea why anyone else would be interested in this. Just got distracted in GeoGebra… so it’s on the Tube.

3 Piece Hexagonal TessellationI was looking at the standard (yet beautiful) isometric rhombus tessellation in tile on some floor, and got wondering about how it would look for non-isometric parallelapipeds. Started to make it in GeoGebra and realized that of course I wanted to be able to make Escher style edge alterations.

Hope you can make something pretty! On GeoGebraTube.

Polygon Portal.

Thinking about ways to make a nice polygon spiral. This one is created by rotating and dilating the point that determines the first rotated polygon. (Using matrix exponentiation to rotate around the origin.) I love the spiral and 3-D effect of the transformation.

On GeoGebraTube.

This sketch visualizes the following, found at Pat Ballew’s always interesting math history blog.

Hugh Worthington, “An essay on the Resolution of Plain Triangles, by Common Arithmetic.” appearing in
“A Wealth of Numbers: An Anthology of 500 Years of Popular Mathematics Writing” by Benjamin Wardhaugh.
“half the longer of the two legs added to the hypotenuse, is always in proportion to 86 as the shorter leg is to its opposite angle. ”

You must want to see for yourself, so here’s the GeoGebra.