# [plt-scheme] The Philosophy of DrScheme

Hey, looks like a cool book, thanks for sharing it.
On Tue, Dec 2, 2008 at 7:27 AM, Daniel Prager <danprager at optusnet.com.au> wrote:
>*
*>* 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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*
--
Eduardo Bellani
www.cnxs.com.br
"What is hateful to you, do not to your fellow men. That is the entire
Law; all the rest is commentary." The Talmud