Triangle -- from Wolfram MathWorld

A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same. The sides of a triangle are given special names in the case of a right triangle, with the side opposite the right angle being termed the hypotenuse and the other two sides being known as the legs. All triangles are convex and bicentric. That portion of the plane enclosed by the triangle is called the triangle interior, while the

Third Brocard Triangle -- from Wolfram MathWorld

Using Wolfram, Alpha to Understand Mathematics

Malfatti Triangle -- from Wolfram MathWorld

Archimedean Graph -- from Wolfram MathWorld

Circumtangential Triangle -- from Wolfram MathWorld

Integer Triangle -- from Wolfram MathWorld

Circle Packing -- from Wolfram MathWorld

Schoute Center -- from Wolfram MathWorld

First Morley Adjunct Triangle -- from Wolfram MathWorld

Obtuse Triangle -- from Wolfram MathWorld

Euler's Number Triangle -- from Wolfram MathWorld

Waring's Problem -- from Wolfram MathWorld, four square theorem

What is the simplest-to-understand proof of the existence of the