The Pythagorean Theorem - Educational Outreach

One example of a periodic process is the time/distancebehavior of a piston in a gasoline engine as it repeats thesame motion pattern some 120,000 to 200,000 times in anormal hour of operation. Our human heart also exhibitsrepetitive, steady, and cyclic behavior when in good health.Thus, the heart and its beating motion can be analyzedand/or described using ideas from modern trigonometry ascan any electromagnetic wave form.Note: On a recent trip to Lincoln, Nebraska, I calculated that thewheel on our Toyota would revolve approximately 1,000,000 timesin a twelve-hour journey—very definitely a cyclic, repetitive process.Returning to measurement of distance, look up tothe night sky and think ‘how far to the stars’—much likeour technical ancestors did in ancient Greece, Rome,Babylon, etc. Trigonometry has answered that question inmodern times using the powerful parallax technique. Theparallax technique is a marriage of modern and old: careful,precise measurement of known distances/anglesextrapolated across vast regions of space to calculate thedistance to the stars. The Greeks, Romans, andBabylonians would have marveled! Now look down at yourGPS hand-held system. Turn it on, and, within a fewseconds, you will know your precise location on planetearth. This fabulous improvement on the compass operatesusing satellites, electronics, and basic trigonometry asdeveloped from right triangles and the associatedPythagorean Theorem. And if you do not have a GPS device,you surely have a cell phone. Every fascinating snippet ofcellular technology will have a mathematical foundation intrigonometry and the Pythagorean Theorem.Trigonometry rests on five pillars that areconstructed using direct Pythagorean principles or derivatesthereof. These five pillars serve as the foundation for thewhole study of trigonometry, and, from these pillars, onecan develop the subject in its entirety.Note: In 1970, while I was in graduate school, a mathematicsprofessor stated that he could teach everything that there is to knowabout trigonometry in two hours. I have long since realized that heis right. The five Pythagorean pillars make this statement so.117