Sangaku Synchronicity.
I love the Japanese sacred geometry known as sangaku. As I was preparing for a class on proof in HS geometry, I was thinking about what could add a level of intrigue to the circle, triangle and parallel line proofs - and thought of sangaku. I became quite taken with the 5 circles in a square one pictured above; beautiful Pythagorean Theorem connections.
I was pretty stumped working it out, so I set it up in GeoGebra to trace the possible squares - and found that gorgeous limaçon hiding! Wow!
So then I had to work up the whole thing in GeoGebra. Serendipity in math is a sweet thing, no?
If you’d like more, Jean-Paul Berroir has some gorgeous Sangaku on GeoGebraTube











