Subject: Angles Name: Rayna Who is asking: Student Level: Secondary
Question:
Thanks, Hi Rayna, I have three suggestions. One from Claude: How about talking about pool? There are a lot of sites in the games sections of browsers (at least yahoo), and some of them talk about the mathematical aspects, like the angles and so on. and two from Walter: My suggestions for interesting 'angle' projects would be to move one from the plane to look at angles in other situations. Here are TWO possibilities: - Angles on the Sphere.
The sum of the angles of a triangle on a sphere is always >= 180 degrees. Infact, if you know this sum you can compute the area (sum 180 degrees means the area is 0!). Moreover, if two traingles have the SAME three angles, then they are congruent: AAA congruence - rather like SSS congrunce in the plane. You could probably prove the angle sum / area formula for the sphere, within a project. A possible source is: http://www.math.cornell.edu/~dwh/books/eg99.htmlThis is a draft textbook for first year university geometry - but only assumes about grade 11/12 math (no calculus or linear algebra). - Angles in polyhedra.
Take the regular polyhedra. Add up the angles in all the faces. Now consider adding up the 'angle deficits': At each vertex find out how much LESS than 360 (a flat full circle) the sum of the angles in the faces is. Add up these deficits. You should find that the sum of these deficits is the SAME for all the regular polyhedra. Consider other non-regular polyhdra. Find the same angle deficit sum. There is a theorem lurking in this constant. It is related to 'Euler's Formula'. (What we are doing is actually older than Euler - it goes back to Descartes.) A search on the internet under Euler's Formula should give some information on these results.
The Centralizer |