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Proofs Resources

Blogs

Rigor is something that is emphasized frequently in higher levels of mathematics and physics, and it has always been something that I appreciated. Unfortunately, with increased rigor often comes a decreased number of people who can understand an argument. One pedagogical ploy that has been used to great effect has been to offer "proofs" of rather difficult concepts on the basis... read more

Blogs

Proof of the Assertion that Any Three Non-Collinear Points Determine Exactly One Circle This is an interesting problem in geometry, for a couple of reasons. First, you can apply some earlier, basic geometry principles; and secondly, you can choose two different strategies for solving the problem. The basic geometry underlying: any three non-collinear points determine a plane, somewhere... read more

Blogs

In mathematics, we start with the natural numbers (or more simply the 'counting' numbers) and learn how to count, starting with 1 and moving up the positive number line. But something special about counting numbers is usually overlooked- primes.    Looking at the naturals, we have {1, 2, 3, 4, 5, 6, 7, ... }  all the way to infinity.    Now if you pick... read more

Lessons

Proving Quadrilaterals Are Parallelograms In the previous section, we learned about several properties that distinguish parallelograms from other quadrilaterals. Most of the work we did was computation-based because we were already given the fact that the figures were parallelograms. In this section, we will use our reasoning skills to put together two-column geometric proofs... read more

Lessons

Writing Two-Column Geometric Proofs As we begin our study of geometry, it will be necessary to first learn about two-column proofs and how they will us aid in the display of the mathematical arguments we make. All areas of math become quite complex or confusing in one way or another. However, writing solutions in the form of a two-column proof will not only allow us to organize our... read more

Lessons

Derivative Proofs Though there are many different ways to prove the rules for finding a derivative, the most common way to set up a proof of these rules is to go back to the limit definition. This way, we can see how the limit definition works for various functions. We must remember that mathematics is a succession. It builds on itself, so many proofs rely on results... read more