Mathematics is a fascinating subject. Delve deeper into its nuances and intricacies, and you’re likely to fall in love with it. Vast, confounding and yet, mesmerizing, Maths holds its followers in thrall.
An important aspect of Maths is its various interesting theorems, corollaries and principles, out of which, the Pythagoras Theorem holds special place in the scheme of things.
History Of The Pythagoras Theorem
The Pythagoras Theorem was named after the ancient Greek mathematician Pythagoras, supposedly the first to offer a proof of the theorem. The first written record of the proof appears in Euclid’s mathematical treatise, ‘Elements’, some 200 years after Pythagoras discovered it. Today there are around 600 proofs of the theorem and numerous corollaries too.
This theorem was one of the earliest concepts known to ancient civilizations. Although Pythagoras is credited with the discovery of the principle, people in other ancient cultures had noticed the special relationship between the sides of a right triangle long before Pythagoras.
Four ancient clay tablets from Babylonia from 1600 B.C.E., some 1000 years before Pythagoras, suggest that the Babylonians had already realized the special nature of the theorem. This theorem is also mentioned in the Baudhayana Sulba-sutra of India, written between 800 and 400 B.C.E. The Chinese too had some inkling of the theorem in ancient times.
What Exactly Is The Pythagoras Theorem?
The Pythagorean Theorem states that the sum of the squares of the lengths of the two other sides of a right-angled triangle is equal to the square of the length of the hypotenuse. In mathematical terms, if in a right-angled triangle, a and b are the sides that include the right angle, and c is the hypotenuse, then,
a2 + b2 = c2
This relationship plays an important part in many fields of mathematics. It plays a leading role in Geometry, forms the basis of Trigonometry, and in its arithmetic form it connects Geometry and Algebra.
Uses Of The Pythagoras Theorem In The Real World-
The Pythagoras theorem is used extensively in Physics, engineering, architecture, construction surveying, navigation and various other fields. Any physics that involves the concepts of length, distance, rotation, angle, makes use of the Pythagoras Theorem in some way or the other.
Architects and engineers use the Pythagoras Theorem to calculate the length, structure, heights of bridges, ramps, walkways, slopes of roofs etc. They also use it to ensure that buildings are square. Often, when laying the foundation for the corners of a building, one of the methods they use is based on this theorem.
Oceanography uses the Pythagoras Theorem to determine the speed of sound in water, calculate the range of a sound source in water and various other uses.
Car navigation systems make use of the theorem to pinpoint locations. NASA uses triangulation, based on the Pythagoras Theorem, to determine the position of spacecraft. NASA sends a signal to the craft which then bounces the signal back. These figures are used to calculate the craft’s location in space.
The Pythagoras Theorem is used for two-dimensional navigation for ships and aircraft to determine distances in the case of ships, and ascent and descent in the case of aircraft.
The Pythagorean Theorem is used in surveying to calculate the steepness of slopes of hills or mountains. It can also be used to measure the length of water-bodies, bridges etc.