Proof That The Sum The First N Odd Integers is a Square

The sum of the first n odd integers is a square. This is a theorem and can easily be proven if you have already learned proof by mathematical induction. Even though it sounds like a boring theorem, it is actually very interesting if represented visually. Consider the following diagrams and their numerical representations.

1+3=4

$latex 1 + 3 = 2^2$

 1+3+5=9

$latex 1 + 3 + 5 = 3^2$

Can you see the pattern? Let’s have some more examples.  Continue reading

New Series: Math Proof of the Week

I am starting a new series called Math Proof of the Week. This is very similar to Problem of the Week of the many websites on the internet. Each week, I will be giving a challenging mathematical proof problem which is accessible for high school students. The solutions of will be given the following week.

The problems will be given every Friday. This will give students weekend to cobble and solve the proof. The proof problems will involve the basic proofs in Algebra, Geometry, Number Theory, Elementary Calculus, Probability and Combinatorics. Of course, the problems are slightly more challenging than the ones I’m discussing in this blog.

Image Credit: http://animalluverclub.wordpress.com/