# [plt-scheme] The Philosophy of DrScheme

 From: Daniel Prager (danprager at optusnet.com.au) Date: Tue Dec 2 04:27:46 EST 2008 Previous message: [plt-scheme] Re: The Philosophy of DrScheme Next message: [plt-scheme] The Philosophy of DrScheme Messages sorted by: [date] [thread] [subject] [author]

```On 02/12/2008, at 5:26 AM, Greg Woodhouse wrote:

> A minor nit: There is no reason why mathematics cannot be taught as
> an active process of discovery. The problem (well, one problem) is
> that the only way to really learn mathematics is by doing, and that
> means calculating. Still, there is no reason it can't be
> interesting. I'll give you an example: one thing that always
> intrigued me, even as a child, is that there are only 5 regular
> polyhedra (the tetrahedron, octahedron, cube, dodecahedron and
> icosohedron), but I didn't realize until much later how accessible a
> result it really is. You could almost make it a homework exercise!
> Start with Euler's famous formula V - E + F = 2 (for a topological
> sphere) and then suppose you have refgular polyhedron the faces of
> which are n-gons. It all comes down to counting: If there are m of
> them, how many times will you count each vertex in m times n
> vertices per face? How many times will you count each edge? What
> happens if you plug these numbers in Euler's formula? Even if youer
> students take euler's formula on faith, the result is still
> impressive.
>

An aside:

Greg's example of Euler's formula is used to good effect in a
wonderful book by Lakatos, "Proofs and Refutations", that reads almost
like a play about what an idealised mathematical classroom might look
like.  [If you "look inside" on Amazon, you can read the first few
pages, which gives the flavor of the book.]

```

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