Subject: Geometry

Geometry

What is Geometry?

Wikipedia defines Geometry as "a part of mathematics concerned with questions of size, shape, relative position of figures, and properties of space." Famous mathematicians such as Euclid (who created Euclidean Geometry), and Descartes (created the Cartesian Coordinate System), furthered the advancement of knowledge in the field of Geometry.

In the beginning Geometry could be used to measure the lengths between cities, the area of ones land, the volume of a necessary construction material. Later, more advanced forms were used in the field of astronomy and mapping the positions of stars and planets. Geometry advanced even further to become one of the building blocks of calculus in the 17th century. In modern times, Algebro-geometric methods are used in particle physics (i.e. String Theory).

Okay, can you throw me a bone here, I need an Example..

It's 5000 BC, and you've just been commissioned to build a rather large and in charge pyramid for your pharaoh. The first step is for you to determine how much limestone you will need to have shipped up river from the quarry to build your glorious pyramid. You know the base of the pyramid needs to be big, very big, for your pharaoh to be pleased. You decide that if the base is 600 ft on each side and 400 ft tall, there wouldn't be another structure withing 100 miles that could trump this grand structure. But how much limestone would a structure of that size need to be?

Well your local geometry teacher has instructed you that the volume of a pyramid is the area of the base time the height divided by 3, or:

Area_{base}*height\over3

And now you can put your order in for 600 ft * 600 ft * 400 ft / 3 = 48,000,000 ft3 of limestone.

I get it! Teach me more!

Below is an intimidating list of all areas of Geometry; don't sweat it if this looks like a foreign language. Take the topics one at a time (they start with the basics and get more difficult the further along you get), and you may find the subjects build upon one another, just like your teachers explained in every math class you've ever taken.

You can rely on your knowledge from past math courses, or you can browse the collection within the math^2 website to help brush up on any related subject matter. Let's get started!!

Geometry Building Blocks?

  1. Geometry words & Symbols
  2. points, lines and planes
  3. Line segments
  4. Coordinate Geometry
  5. Pairs of lines - parrallel, perpendicular, intersecting, bisecting, etc
  6. Classifying angles, obtuse, acute, right, pairs of angles, complimentary & supplementary
  7. Angles and intersecting lines
  8. Measurement, bisecting, and transposing lines?
  9. Measuring chords & arcs
  10. Circles, circumference, formulas for radius, pi, area, area of sector

Postulates and Theorems?

  1. Angles
  2. Triangles
  3. Parallels
  4. Quadrilaterals
    1. Parallelograms
  5. Circles
  6. Theorems and Postulates?

Polygons?

  1. Polygon basics
  2. Angles in Polygons
  3. Perimeter and Area
  4. Calculating Distances?
  5. Sides in polygons with known angles
  6. Quadrilaterals
  7. Area of polygons and circles

Triangles

  1. Right, isosceles & congruent
  2. Prove triangles are congruent by SSS, SAS, HL, AAS, ASA?
  3. Midsegment Theorem and Coordinate Proof?
  4. Use Perpendicular Bisectors?
  5. Use Medians and Altitudes?
  6. Use Angle Bisectors of Triangles?

Relations and Sizes?

  1. Congruent figures
  2. Similar figures?
  3. Squares and square roots
  4. The Pythagorean Theorem and right triangle facts
  5. Properties of transformations?

Three-dimensional Figures?

  1. Space figures?
  2. Calculating Volume?
  3. Prisms?
  4. Pyramids?
  5. Cylinders, cones, and spheres?