Shower thought after chatting with @Jack Rusher: we delay teaching kids geometry until we can trust them not to poke someone's eye out with the pointy end of a compass. Here's a little program to do compass-and-straightedge geometrical construction on a computer: https://gist.github.com/akkartik/20a0c7e7589c6179666fc78bc04b28b4 Pictured below: constructing a second line (in black) parallel to a given line (red) passing through a given point.

Aside:

we delay teaching kids geometry until we can trust them not to poke someone's eye out with the pointy end of a compass

That... can't be true!? That beggars belief! It's a cute story, but there are countless geometric things that kids learn long before they get to play with compasses.

I can record a little video later today 👍🏼 Whoa, Replit handles Love2d?!

Yeah, AGG is the GOAT

Dr GEO is a smalltalk geometry environment https://www.gnu.org/software/dr-geo/ https://www.youtube.com/c/DrgeoEu/videos

"You can modify its own source code while using it." 🤯

I like Dragonbox Elements https://dragonbox.com/products/elements. It's not about geometry, not really; but it does two related things: (1) Categorizing objects based on their properties e.g. a quadrilateral is a figure with four strait sides, in a trapezoid one pair of sides is parallel, in a parallelogram both pairs of sides are parallel. (2) Constraint propagation e.g. line a is parallel to line b, line b is parallel to line c, so line a is parallel to line c.

@Ivan Reese My contention in the conversation @Kartik Agaram mentioned was a bit differently shaped. Basically, I think almost all real mathematical intuition is geometric in character and we do people of all ages a disservice by teaching them notation and algebraic procedures for manipulating symbols without developing their intuition.

"One of the ways Papert used Piaget’s ideas was to realize that young children are not well equiped to do “standard” symbolic mathematics until the age of 11 or 12, but that even very young children can do other kinds of math, even advanced math such as topology and differential geometry, when it is presented in a form that is well matched to their current thinking processes. The LOGO turtle with its local coordinate system became a highly successful “microworld” for exploring ideas in differential geometry."

Oh yes, @Jack Rusher bears no blame for my brain farts in the shower. One epiphany I had after our conversation (again don't blame him, though!) is that text vs visual/graphics is not a very useful framing. What matters is grammar and geometry.