# DS7: So a circle is just a very large number of very short lines

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I rarely do any organized academics with DS5 who is in still in 3 day play based preschool. DS7 was working on some MEP2 worksheets on order of operations and paper folding. He finished early and was going on about how coloring in the sides on the paper folding exercise was fun but to easy while DS5 and I worked on such heady problems as what 7-3 might be...

DS7 then moved on to looking at DS5's last hand drawn worksheet on shapes with triangles, squares, pentagons, hexagons, and red stop signs... Then he comes out with his "So a circle is just a very large number of very short lines"... Err, umm... yes. We talk about different n-gons and he observes that the more sides you add the closer you get to a circle. We talk about having an arbitrary number of sides to approximate a cicrle... We even do a few inscribed diagrams to confirm his intuition. I then move on to discussing continuous functions. It is clear he views this as merely a clever trick if you happen to have a piece of string. I then pivot to discussing simple orbits and he allows as how you could get natural circles similar to his model... OK, great we can leave it there for today ;).

DS7  has clearly intuited a concrete version of the circle. Classsical geometers are rolling over in their graves but I'm perfectly happy to pitch Donald Knuth against Euclid for now.

It is clear, he is sooo ready for the logo/scheme/python programming activities I have planned for this summer. Clearly the first few projects will just be about syntax and demonstrating concepts he already grasps... Likewise I was planning on doing some compass and straightegde constructions and basic geometry at the same time. As usual, DS is forcing the issue rather than allowing me to gradually introduce advanced concepts... So it goes.

I am just so amused.

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He might like this

http://aleph0.clarku.edu/~djoyce/java/elements/elements.html

It is a dynamic website illustrating Euclid's Elements 13 books.

My son is much more geometry than Algebra as well. People have warned up one side and down the other that geometry is not appropriate for a nine year old. The kid is taking to proof based geometry so fast it is crazy.

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