# Geometry

We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.
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# Perimeter, area, and volume

A broad set of tutorials covering perimeter area and volume with and without algebra.
All content in “Perimeter, area, and volume”

## Perimeter and area of triangles

You first learned about perimeter and area when you were in grade school. In this tutorial, we will revisit those ideas with a more mathy lens. We will use our prior knowledge of congruence to really start to prove some neat (and useful) results (including some that will be useful in our study of similarity).

## Triangle inequality theorem

The triangle inequality theorem is, on some level, kind of simple. But, as you'll see as you go into high level mathematics, it is often used in fancy proofs. This tutorial introduces you to what it is and gives you some practice understanding the constraints on the dimensions of a triangle.

## Koch snowflake fractal

Named after Helge von Koch, the Koch snowflake is one of the first fractals to be discovered. It is created by adding smaller and smaller equilateral bumps to an existing equilateral triangle. Quite amazingly, it produces a figure of infinite perimeter and finite area!

## Heron's formula

Named after Heron of Alexandria, Heron's formula is a power (but often overlooked) method for finding the area of ANY triangle. In this tutorial we will explain how to use it and then prove it!

## Circumference and area of circles

Circles are everywhere. How can we measure how big they are? Well, we could think about the distance around the circle (circumference). Another option would be to think about how much space it takes up on our paper (area). Have fun!

## Perimeter and area of non-standard shapes

Not everything in the world is a rectangle, circle or triangle. In this tutorial, we give you practice at finding the perimeters and areas of these less-than-standard shapes!

## Volume and surface area

Tired of perimeter and area and now want to measure 3-D space-take-upness. Well you've found the right tutorial. Enjoy!