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Daily Archives: January 19, 2011

Math Teachers at Play Blog Carnival Deadline

Posted on January 19, 2011 by Guillermo Bautista | Leave a comment

Mathematics and Multimedia will be hosting the Mathematics Teachers at Play Blog Carnival #34. If you have articles or blogs about anything mathematics, you can submit it here. The deadline of submission will be on January 19, 2011, and the post date will be on January 21, 2-11.

The Mathematics Teacher at Play was organized by Denise of Let’s Play Math.

You may also want to read the following posts:

Wanted: Carnival Hosts

If you are a blogger and you wanted to promote your blog, hosting a carnival is one of the most effective ways. If you are interested to host the Mathematics and Multimedia Carnival, contact me at mathandmultimedia@gmail.com.

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Posted in Blog Carnival

Tagged blog carnival, blog carnival host, let's play math

The Infinitude of Pythagorean Triples

Posted on January 19, 2011 by Guillermo Bautista | 4 Comments

In the Understanding the Fermat’s Last Theorem post, I have mentioned about Pythagorean Triples. In this post, we will show that there are infinitely many of them. We will use intuitive reasoning to prove the theorem.

For the 100th time (kidding), recall that the Pythagorean Theorem states that in a right triangle with side lengths $a, b$ and $c$ , where $c$ is the hypotenuse, the equation $c^2 = a^2 + b^2$ is satisfied. For example, if we have a triangle with side lengths $2$ and $3$ units, then the hypotenuse is $\sqrt{13}$ . The converse of the Pythagorean theorem is also true: If you have side lengths, $a, b$ and $c$ , which satisfies the equation above, we are sure that the angle opposite to the longest side is a right angle.

Are we a Pythagorean Triple or not?

We are familiar with right triangles with integral sides. The triangle with sides $(3, 4, 5)$ units, for instance, is a right triangle. This is also the same with $(5, 12, 13)$ and $(8, 15, 17)$ . We will call this triples, the Pythagorean triples ,or geometrically, right triangles having integral side lengths. Continue reading →