I don’t want to bore you, I just want to give you a small glimpse into the things in life that I enjoy. Today I was in class and the professor brought up circles and the ancient Greeks, and I got thinking about this beautiful and amazing property of triangles, that when you draw the diameter and then pick ANY point on the circle and connect it to the ends of the diameter to form a triangle, you will always make a right triangle. I know this is because the angle you make will always be half of the “intercepted” arc, and since a diameter forms an 180 degree arc, then you will be making 90 degree angles (right angles). But I wanted to know if it is possible to prove this without using that fact. I really wanted to convince myself of this, that it is not “magical” (although it’s still beautiful).
So, as long as you passed geometry and algebra in high school, you should be able to follow this 🙂