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Logic and Proof

Logic and Proof

Logic and Proof Resources

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Euclid's Definitions and Postulates

We're studying Euclidean geometry and this website gives a list a pretty thorough (and well-organized) list of all of Euclid's geometric original definitions and postulates. The writing is a bit flowery, but not difficult to follow. If you're achin' for some Euclid, this website will be heaven on earth (or the Internet).

eHow: How To Do Formal Geometry Proofs

If proofs have got your knickers in a twist, this website will lay it all out for you. Complete with helpful tips and a full set of instructions, it'll get you started chipping away at proofs sooner than you can say, "formal geometry proof." Thanks, eHow!

Theorems and Postulates

If you understand the idea of proofs, but can't quite keep the properties and postulates and theorems straight, this might help you out a bit. Not only does it clearly list out a bunch of handy dandy theorems and postulates, but it also categorizes them so you can find whatever you're looking for without a giant magnifying glass.

A Background of Constructivism

The whole basis for our logic and reasoning is that these shapes, lines, and stuff can be measured. This is based in the idea of constructivism. Want more information from the wonderful (and very scholarly) world of academia? You got it.

Purplemath: Induction Proofs

Induction got you in a dither? Let the fine folks at Purplemath help bulk up your induction chops.

Dr. Math: Proof by Induction

Proving stuff by induction can be known to cause headaches, stomach cramps, and spontaneous yelling. Let the good Doctor prescribe you some solid practice, and you'll be feeling tip-top in no time.

Art of Problem Solving: Proof by Contradiction

A short-and-sweet breakdown of how proofs by contradiction work, including Euclid's famous proof that there's an infinite number of prime numbers.


Yay Math: Intro to Proofs

Watch Mr. Robert Ahdoot, a high school math teacher (and multi-gazillionaire) as he explains the properties of equality and introduces proofs. As he says, proofs are probably one of the most difficult concepts in geometry, so hopefully his flashy bling isn't too distracting.

MathPlanet: If-Then Statements

If the fact that math can make statements seems fundamentally wrong to you, we understand. Fortunately, there's a whole planet (or a website masquerading as a planet, anyway) dedicated to math and helping us understand these statements. If you watch the videos and explore the various topics, then it'll all come together. Did you catch that if-then statement?

Proof by Mathematical Induction

Listen to Paul's dulcet tones as he takes you step-by-step through a slightly more complicated proof by induction. Paul is good people.

Spoonful of Maths: Proof by Contradiction

In this video, Dr. Herke runs us through a proof that there's no smallest rational number greater than zero. Say what? It's a seriously weird idea, but contradiction is your friend here.

Games and Tools

Two-Column Proofs Practice Tool

If you feel comfortable enough with definitions and angles and lines and stuff, you may want to give this tool a try. It's just like Build-A-Bear, except in this case, you're building a proof. It won't protect you from monsters while you sleep, but it will protect you from failing geometry. Fill in the statements and the reasons from the options provided and conquer those proof-monsters in no time.

ClassZone: Geometry Quizzes

Practice makes perfect (unless you're doing it wrong). Testing yourself and getting instant results? There's no way to do that wrong. Choose any subject you feel confident or helpless about and complete the online quiz. It'll tell you if you're a master in that area, or if you might need a little more practice before you're ready to tackle a full-on test.

Math Goodies: Conditional Statements

If you're struggling with conditional statements and how to represent them, especially, take a gander at this. It'll give you thorough explanations with charts and everything, plus a mini-quiz at the end. Feel free to explore other topics in the unit if you feel a little uneasy with the material. No need for a permission slip.


Need more help minding your p's and q's? This quick little game will enable you to tell the difference between a converse and a contrapositive without breaking a sweat. Drag the definition to match the symbols as fast as you can, and your p's and q's will have minds of their own. Not really though, because that'd be weird.

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