-------Math Home -------
Here I am going to show 2 problems. They might not have anything in common, other than the fact that they use elementary mathematics and the emphases is placed on geometry. Everything numerical has a geometric explanation. This explanation is often much simpler than solving using pure numbers and equations. So the more a problem relates to geometry, the easier it is to relate it to something tangible like the things we see in every day life. This is nothing new.
It is sort of addition with geometry; you only need basic math and a little imagination to redraw shapes. It is as simple as doodling on a page. The only catch is that the shapes you create must have meaning. There has to be a reason behind the shape. It’s back to the basic shapes we learned in grade school.
When I wanted to play with Prime numbers, I used geometry. Granted it is just a concept and may not work, but I searched for a solution from the geometry. It would take a lifetime of math knowledge of advanced mathematics, but I turned to the geometry to look for something more tangible that could have been missed.
Now however, we will concentrate on 2 little, new problems.
On to the problems:
This problem was excerpt from: UMAP Jornal: The Solar Concentrating Properties of a Conical Reflector, Don Leake, Page 3
Here we will solve number c: h as function of theta, R and r;
This problem was excerpt from: “Analytic Trigonometry with Applications”, Barnet; Ziegler, Page 37 problem 37
I’m working on a new section for Constructor’s Corner called: “Corners” It will feature work from other Constructors. That is anyone who wants to email about projects. I would also like to get math/design problems from more people over the Web.
The next problem was recommended to my by a friend: C. Blanco. He was looking for different ways to solve it. That is other than the obvious Pythagorean Theorem. My interest was to use the Scosine. Although, this may lead to a more complicated way. Or you could use similar triangles. The key thing to note is the problem solving process. These 2 problems are just an effort to share these problems while trying to show a non standard approach to a problem that would appear ordinary by other means.