Can’t believe this was the Bizarro cartoon for today. Off to Twitter Math Camp!
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.
Two curves cut all circles at right angles: straight line and a tractrix.
I didn’t know what a tractrix was, so I Googled it! Tractrix definition from Wikipedia: Tractrix (from the Latin verb trahere ”pull, drag”; plural: tractrices) is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a tractor (pulling) point that moves at a right angle to the initial line between the object and the puller at an infinitesimal speed.
Here’s a gif from Wikipedia showing a tractrix being created from dragging a pole:
painting with circle intersection-chords
Reblogged for further study.
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).