Beautiful Minds

A²+B² = C². This formula that we have all learned about at one point in our lives is integral to all geometric calculations and mathematical applications in general. Although we are familiar with the formula, not many of us know anything about the man who derived this important formula. This person was none other than the legendary Greek philosopher, mathematician, and founder of the Pythagorean Brotherhood and theorem: Pythagoras of Samos. 

Pythagoras lived approximately between 570-495 BCE when Greece was counted among its population great philosophers and mathematicians. He established a school in Croton, now in Italy, where his Pythagorean followers studied mathematics, music, and metaphysical issues. This group treated math not only as an instrument for making calculations but as a way to view the world. Not much is known about Pythagoras (in comparison to other great mathematicians of his time) because there were no written records about him and his society was sworn to secrecy.

Pythagoras thought that numbers were the foundation of all things. This was a revolutionary idea that led to the development of fundamental ideas related to mathematics philosophy. Harmony, proportion, and indivisibility of the universe were embodied through his instruction, and these very ideas are reflected in more current science.

One cannot have a conversation about Pythagoras without making reference to the Pythagorean Theorem, which is perhaps his most well-known contribution to the world. This principle that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the legs is one of the most frequently used formulas in all of mathematics, and serves to advance our current world in a variety of different ways. 

While evidence seems to indicate that related ideas were practiced in Babylonian and Indian mathematics, there is no doubt that it was Pythagoras, together with his followers, who was the first to demonstrate it with rigor. This theorem is much more than just a formula; it is a law. This law is not just used by students like me during school and competition math like the AMC, but also by architects, engineers, scientists, and even NASA to derive measures, construct scenarios, and even plan space expeditions. Moreover, when you use a GPS device to navigate, the Pythagorean Theorem is working behind the scenes to pinpoint your location. GPS relies on a process called triangulation, where signals are sent from at least three satellites orbiting Earth. Each satellite transmits its position and the time the signal was sent. By calculating how long the signal takes to reach your device, the distance to each satellite can be determined. These distances form overlapping spheres, and your location is found at their intersection. To refine these calculations, the Pythagorean Theorem is applied repeatedly, helping to determine precise distances in a three-dimensional space. This mathematical process enables GPS to display accurately not only your location but also your altitude, speed, and the shortest route to your destination.

Pythagoras was also captivated by numbers, which led him to the study of music. In turn, he found that harmony is controlled by mathematical relationships. For instance, one may perceive an important discovery in the science of acoustics by adhering to the rules of string tension, whereby cutting strings into harmonic ratios creates pleasant sounds. Through my experience with music, another rule I have discovered is that going one octave up is the same as doubling the frequency in hertz of a sound, and that our current piano system uses an equilibrium of 2(¹/¹²) frequency different per note in order to ensure equal transposition among key signatures.  His work integrated math and aesthetics and impacted different areas including physics and composing music.

Pythagoras is supposedly the first to invent the term ‘philosophy,’ which means “love of wisdom.” On another note, his faith in the transmigration of souls, reincarnation, and the view of the cosmos as an order is something that sustained Western thinking for several centuries. When we use the Pythagorean theorem and reflect on his contributions, we should remember him for his unique approach as both a mathematician and a philosopher, the intentional care in the preservation of his great works, and the foundation that he provided for all geometrically shaped things in our world today.

So, the next time you turn on your GPS to drive to your destination, remember to thank Pythagoras for helping you find your way.