Geometry

A common geometry problem involving a triangle.

“Geometry? More like yo mammatry!”
~ Euclid on Geometry

Geometry, in a modern sense, is the art of proving that any two triangles are congruent; and therefore, by extension, all triangles are congruent. However, there are many different branches of geometry involving the study of objects that failed to be triangles, objects that wanted to be triangles but couldn't, and ex-triangles.

There are three kinds of geometry, Hyperbolic Geometry, Elliptic Geometry and Bernhard Riemann, each having applications to different kinds of space. Bernhard Riemann applies when in German Space, a particular form of space in Europe. Hyperbolic Geometry applies when you're in the water, or thinking about special relativity, and Elliptic Geometry applies in all other circumstances.

The Eight Basic Geometric Theorems about Triangles

SSS
SSA
SAS
SAA
ASS The ability of one to use this theory has been highly disputed, because some students find it offensive, though most find it amusing to hear their teachers say it.
ASA
AAS
AAA

The proofs of Theorems 2 and 5 are left as an exercise to the reader.

Basics

There are no basics.

History

The Origins of Geometry

Geometry originated as an early Greek attempt at a human genome project. However, the Greek, not speaking English and writing their literature without the aid of spellcheck quickly found themselves giving birth to a new word. This new word came to be appended to mathematics that made particularly little sense, until Newton invented the word 'calculus' to use instead.

The Discovery of Triangles

Blaise Pascal is credited with being the first to discover that he could draw three lines that didn't go through the same point. Unfortunately, Pascal was better at drawing than counting, and in an attempt to count the twelve angles (4 per intersection) he reached the total of three. Not wanting to be responsible for a word with 3 consecutive vowels, he borrowed the 'tri' from 'tricycle' to form the word 'triangle', which today is generally accepted as any shape that can be drawn using lines.

Geometry in the 1800s

In the late 1800s, the self-proclaimed Lord Kelvin theorized that other shapes other than triangles could be drawn. However, the church being already aware of crosses, had Lord Kelvin excommunicated from the church for such blasphemy. With the general acceptance of Euclid that Geometry took an ironic twist.

The Break up of Geometry and Current Geometry

Geometry, in the midset of confusion, broke into many different sects. Euclidean Geometry considered Euclid as a saint, and focused upon his mathematics with a religious fanaticism. They are responsible for concepts such as ordinals, cardinals, and friars. Carl J. Ellipse, lead many geometers to develop Elliptic Geometry, which is widely considered the geometry of curvy objects. Lastly, Hyperbolic Geometry also emerged around 1926 in a jazz night club, and is considered the geometry of excessively curvy objects. In recent years, further branches of geometry have also emerged but they are generally regarded as pushovers and phonies.

Famous Impossibilities in Geometry

There is no way to draw a straight line using only a compass and straight edge. (However, in his later years Carl J. Ellipse proved that it is possible by adding a computer and printer to the list of standard tools.)
There is no way to draw a cube without poking your pencil through the paper.
You will never successfully prove the Pythagorean Theorem if asked to do so on a test.
A circle has no sides or corners. It also has infinitely many sides and corners. This is clearly impossible, because you cannot count to zero (let alone infinity).
Zach S. cannot be cooler than Matt B.

Geometry As A Class

While taking Geometry in high school, all of your friends will be placed in the same class with a teacher that doesn't make you do anything but eat 3.14 and have a fun time. You, however, will be placed alone with a bitchy teacher who will make you do extra work. Your teacher will hate you with a passion and will give you an F on every test, regardless of how well you did.

External links

The Geometry of Special Relativity: The Minkowski Space - Time Light Cone