(Mathhombre) Miscellanea

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.

p5art's wave animation in GeoGebra. Post with more info here.

On the GGBtube. Seems like this one would be a good one to remix. What effects can you make? The second one was made by playing with the dynamic colors as a function of the time slider.

Inspired by an animation from Bruce and Katharine Cornwell on triangle centers. (More about the Cornwells.)

As the radius increases, the animation finds points equidistant from the vertices. Is there a single point equidistant from all 3?
On GeoGebra, of course. The conditionals for when to show what were the challenging thing here, and I’m sure you could find a situation where I screwed them up. Also it only really works correctly if the orientation of the triangle is not reversed.

Etch-a-Sketch.

Was thinking about how to generate some randomization to drawing in GeoGebra and this is what I got!

Drag the point to draw, the colored points will orbit around it.
Reset brings the points back close and distributes them around.
Erase does what you’d think.
Trace lets you turn the trace on and off.
The lone checkbox hides stuff to make your pictures pretty.

On GeoGebraTube, please play! Can you think of other ways to make interesting pens?

Face Symmetry.
How symmetrical is Jennifer Lawrence?
Disturbingly, I’d say.
#ggbchat 3 is on images in GeoGebra. July 2nd, 8 pm ET. Be there or… or we’ll check the symmetry of your face. Yeah.
On GeoGebraTube, of course.

Face Symmetry.

How symmetrical is Jennifer Lawrence?

Disturbingly, I’d say.

#ggbchat 3 is on images in GeoGebra. July 2nd, 8 pm ET. Be there or… or we’ll check the symmetry of your face. Yeah.

On GeoGebraTube, of course.