I'm enjoying the process of discovering how a little Math can go a long way. Readers are enjoying mental Math tricks, Math magic, and other simple things that engage children of all ages to see Math with a sense of awe.
One of my very favorite Math web-sites is Antonio Gutierrez' Go Geometry, subtitled "From the Land of the Incas". I can't even begin to describe this site. It has the most beautiful illustrations of geomtric constructions I've ever seen plus a number of challenging geometry problems. One could easily get lost in this site, and spend many enjoyable hours exploring its many sections.
In the videos section of the site I found a link to a You Tube video: How to make platonic solids with gum drops and tooth picks, by Amanda Scharfenberger. Here's the video:
This video is brilliant. I've been wondering for a while now how to make it easy for kids to build geometric solids and here's a video that demonstrates simple construction with simple materials.
Now you have something fun and educational to do with those leftover gum drops from making gingerbread houses!
For those of you who are not familiar with platonic solids, they are convex geometric constructions made up entirely of "regular" polygons, those whose sides are all the same length. It turns out that there are only five platonic solids:
- regular tetrahedron - a pyramid made of four equilateral triangles
- cube (regular hexahedron) - a solid with six square sides
- regular octahedron - an eight-sided figure constructed from equliateral triangles
- regular dodecahedron - a twelve-sided figured made of pentagons
- regular icosahedron - a twenty-sided figure made of equilateral triangles
I recommend that you look at the pictures of the platonic solids in this Wikipedia article in conjunction with watching the video as the details of the constructions are hard to follow in the video and the solids in the Wikipedia article are easier to study, plus each has an animation to help visualize its construction. Plus, the article has two proofs that there are only five platonic solids.
A great and very relevant exploration is to figure out how many gum drops and how many tooth picks it will take to make each construction and the total of each for all five constructions. Glory will be bestowed upon the first person to post a comment on this message with the correct numbers plus an explanation as to how you determined this number. You get extra glory if you figured it out yourself and super extra glory if your solution is elegant.
Those of us who don't want to figure out these numbers will appreciate the efforts of those of you who do so that we may know how many bags of gum drops and boxes of tooth picks we'll need for this project.