What does a 4-dimensional space look like?

We often hear people in physics and mathematics talking about 4-dimensional, 5-dimensional spaces, etc... so what are those spaces? how do we picture these high dimensional spaces?

Similar triangles

Today, we are going to learn about similar triangles. We will use similar triangles to give a proof of Pythagorean Theorem. 

Caveman's multiplication

Today, I am going to tell you a method of doing multiplication by the ancients. I do not remember the name of this method, nor do I know when this method was invented. Let us just call it "the cave-man's multiplication method"!

Morley's Theorem

In a triangle $ABC$, draw the trisectors of the angles $A$, $B$, $C$. These trisectors intersect at $A'$, $B'$ and $C'$ as in the figure below. Prove that the triangle $A'B'C'$ is an equilateral triangle.