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Solving Equations Using the Pythagorean Theorem

Use a^2 + b^2 = c^2 to find missing side lengths of right triangles.

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Cryptic Notes

Credit: FutUndBeidl
Source: http://www.flickr.com/photos/61423903@N06/7557181168/
License: CC BY-NC 3.0

How does your school protect your personal information? How does your bank keep hackers from stealing your money? Organizations and individuals use codes to protect data, a process known as encryption. Some of the strongest encryption methods have their roots in basic mathematics.

Pythagoras, Security Genius

When a computer encrypts information, it puts the data into a new form. To an outside observer, your information has become a random chain of numbers and letters. To make sense of the encrypted data, he would need a key to the code. Hackers try to figure out the keys to various codes, so that they can steal the information you send over the Internet.

The Pythagorean theorem helps some programmers develop encryption methods. They use Pythagorean triples to encrypt and decode data. A Pythagorean triple is a set of three positive integers that form a solution set for the equation \begin{align*}a^2+b^2=c^2\end{align*}. For instance, 3, 4, 5 is a Pythagorean triple. 30, 40, 50 is another example. There are an infinite number of Pythagorean triples. Data encrypted using Pythagorean triples is easy to encode and decode but difficult for hackers to steal.

Credit: Johan Viirok
Source: http://www.flickr.com/photos/viirok/2498157861/
License: CC BY-NC 3.0

As the techniques of hackers grow more sophisticated, computer programmers must develop new encryption methods. They continue to study mathematics, looking for new formulas and patterns that can help them keep your data safe. Encryption is essential for the modern economy. Without these codes, criminals could access your bank account, swipe your personal records, and steal your very identity. They could commit crimes while ensuring that you were blamed. Mathematicians and computer programmers are all that stands between an orderly world and total chaos.

See for yourself: http://www.kpho.com/story/22915446/hackers-have-new-way-to-steal-info-from-smart-phones

Explore More

Watch the video below to find out about a surprising security vulnerability hidden in plain sight. Read the following article to learn about a recent breakthrough in the field of encryption.



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  1. [1]^ Credit: FutUndBeidl; Source: http://www.flickr.com/photos/61423903@N06/7557181168/; License: CC BY-NC 3.0
  2. [2]^ Credit: Johan Viirok; Source: http://www.flickr.com/photos/viirok/2498157861/; License: CC BY-NC 3.0

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