In our modern world, we rarely stop to think about geometry and what it has done for our world. One extremely profound discovery in the study of geometry is the Pythagorean Theorem. Not surprisingly the theory takes the name of the man credited with the first proof, Pythagoras. Thought to live in the sixth century BC, the ancient Greek mathematician was the first to prove the relation of the three sides of a right triangle. This relation is true of the sides of any right triangle, regardless of any other factors you could modify. Written as *a ^{2} + b^{2} = c^{2}*, with the ‘c’ referring to the length of the hypotenuse (the longest side) and the ‘a’ and ‘b’ representing the lengths of the two other sides. The sum of the square of other two sides is always equal to the square of the length of the hypotenuse itself. Hypotenuse, for review, is the side of the triangle directly across from the right angle. Remember that the Pythagorean Theorem will only work with right triangles, which are those including a right angle.

All right angles are those with a measurement of 90°. Think of the angle of intersection of the two lines in an uppercase letter ‘T’ to understand what a right angle looks like. Right triangles are build around these type of angles and the hypotenuse of the right triangle is always the side *directly across from* the right angle itself. Studying **mathematics can be exciting** especially when we are able to understand how the application of our study can be valuable in the real world. Even from a historical perspective, the discovery and related proof of Pythagoras has a profound impact. Creating the impetus for many other fields of study such as Trigonometry, Algebra and Calculus, the Pythagorean Theorem was indeed a very marvelous mathematical breakthrough in it’s time. Our plentiful world, full of engineering marvels is largely due to the knowledge mankind was able to amass since applying the findings of the brilliant Pythagoras. Because a right triangle is the strongest triangular shape known for adding support to a building design, most of the tall structures, bridges and other engineering marvels all can be traced back to the *technology* first introduced in the Pythagorean Theorem today. Interestingly enough, while the work and findings of Pythagoras certainly have great value and merit, there remains some cloudiness and controversy around Pythagoras. It is believed that no remaining texts of Pythagoras remain and that most of the work ascribed to him is only sourced through loose and tenuous connections. Regardless of the validity of the historical framework, the validity and usefulness of the theorem’s teachings are quite notable and quite undisputed by mathematicians all around the world.

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