Points, Lines, Angles, and Planes
Points, Lines, Angles, and Planes Resources
Best of the Web. Picked by our PhDs
Did you know that the columns of the Parthenon aren't actually vertical? Read about how the Greeks used their knowledge of geometry to combat optical illusions. It might inspire you to design a building—or at least wiggle your pencil in a way that makes it look like rubber.
Babylonians are the reason a circle has 360 degrees and an hour has 3600 seconds, not Tony Hawk or Cyndi Lauper. How and why did Babylonians create their complicated number system, and why do we still use it? Learn all about arithmetic—Babylonian-style.
Are Cartesian coordinates really due to Descartes? We may never know for sure, but one thing is certain: Descartes was an awfully bright guy. Read all about the life of a brilliant thinker (a non-Greek one, for once), complete with references and an embarrassing photo. What a looker.
You might think that points, lines, and planes are undefined because they're so intuitive. Not necessarily. Read about the different attempts to define the indefinable according to different classes of geometry. Are they all essentially the same, or are they quite different?
Much of what we learn about geometry in schools is based on Euclid's interpretation of geometrical space. As fascinating and important as it may be, there's more to the world than just Euclidean geometry. Skim through some of these thoughts and musings for a different take on geometry.
A video podcast on the description and naming of points, lines, and planes. These three objects are called "undefined" because it's nearly impossible to have an all-encompassing definition for them. This video gives a really good sense of these objects and it covers collinearity and coplanarity, too.
Tired of listening to monotone voices lecture at you about geometry? This video will clearly show you just about everything you need to know about points, lines, and planes, but it's set to some groovy music. Mute it if you want and watch the slide show, or rejoice in the learning of geometry with some killer dance moves.
Games & Tools
This nifty tool allows you to measure, estimate, and control whatever angles you want. Answer questions, use a protractor, or simply explore the different angles you can make. You don't need a third degree to mess with these angles' degrees.
Find the complementary and supplementary angles as fast as you can to win. You're on a timer, so it's best to think quickly. Don't worry, though, because there's a button you can click if you need help. It'll test not only your complementary and supplementary skills, but it'll hone your arithmetic as well.
This game is more fun than a barrel of monkeys! Rotate the monkey to the given angle and you'll become the top banana in no time. The closer you are to the angle, the more bananas you'll win. After playing this game, you'll estimate angles better than a monkey's uncle. You'll go bananas for it. Hopefully you find the monkey puns a-peel-ing.