Tagged: geometry

Simple wikipedia

This gives simple explanations for things like Pythagoras’ Theorem.

In mathematics, the Pythagorean theorem or Pythagoras’ theorem is a statement about the sides of a right triangle.

One of the angles of a right triangle is always equal to 90 degrees. This angle is the right angle. The two sides next to the right angle are called the legs and the other side is called the hypotenuse. The hypotenuse is the side opposite to the right angle, and it is always the longest side.

The Pythagorean theorem says that the area of a square on the hypotenuse is equal to the sum of the areas of the squares on the legs. In the picture below, the area of the blue square added to the area of the red square makes the area of the purple square. It was named after the Greek mathematician Pythagoras:

If the lengths of the legs are a and b, and the length of the hypotenuse is c, then, a^2+b^2=c^2.

Stringer’s theorem

Stringer’s Conjecture

He’s not in the honors program. His papers, one teacher says, are a mess. In a school where the best and brightest are well dressed, he wears tatty running shoes, jeans, and a brightly colored T-shirt. But Rob Stringer, a high school geometry student in this upscale Boston suburb, has come up with something unknown since Euclid first discovered geometry. With the aid of a computer program developed by researchers at the nearby Massachusetts Institute of Technology (MIT) and Harvard University, he has hit upon a previously unknown geometrical theorem for dividing a triangle into smaller triangles of equal size.


Remarkable achievement by some Americans

giant fractal pecan pie

the thing they don’t tell you about fractals is just how sharp and dangerous they are. i mean, you think you have a pretty good grasp of the mathematical analysis but until a piece of metal with a very high perimiter to surface area ratio tears into your flesh, you’re really missing intuitive appreciation for objects that lack continuous derivatives almost everywhere.

giant fractal pecan pie at instructables
fractal shape allows a much larger pie