Good at Geometry, not so much at Geography

Achild is learning about Egypt, my daughter tells me.  I responded, "Cool!"  That's the country that gave us some amazingly influential math, winding its way from the African continent, around the Mediterranean, into (eventually) Greece. 

Achild made a Phaoroh hat and a water clock, and so I offered her some math that comes from one of my favorite theorems, Thales theorem, named after Thales of Miletus.  (But then, I realized "oh heck, Miletus was in Ionia, not Egypt".  I got Thales confused with Ahmes, the scribe from 1555 BC who wrote what we now call the Rhind Papyrus but which we ought to call the Ahmes Papyrus because Rhind is just the European dude who bought it off of crooks who illegally dug it up.  A whole other story, there).  

At any rate, here's Thales Theorem in action.  (And by the way, thank you for asking, YES it is fun to try to think of a way to explain it to a seven-year old who is great with art but who doesn't do algebra or other fancy formal math yet).  Make a circle.  Fold it in half, so that you get a semicircle. Then make two more folds so you get a triangle with one side along the flat edge of the semicircle, and the other two sides meeting at a corner anywhere along the arc of that semicircle.   

Voila, says Thales.

What Thales says is that that last corner -- where the last two sides meet -- has to be a right angle, same as the corner of a regular piece of paper, no matter where along the arc of the circle you put it.  It's a cool little theorem, that has all sorts of fascinating consequences.

By the way, the word "geometry" is derived from the Greek, meaning "earth (geo) measure (metry)".  As such, it's related to "geography" (earth picture).  But not closely related enough that I remember the difference between Miletus and Africa. sigh.