From the studies that you, perhaps, have learned in school, the person credited to be the one who discovered the Pythagorean Theorem is the Greek philosopher, Pythagoras. However, there are some who say that this is not so.

If you were to study the history of the theorem, you may see that it may not be Pythagoras after all who discovered the Pythagorean Theorem.

The Early History Accounts of the Theorem

In Northern Europe and Egypt during 2500 BC, there were some accounts pointing to an algebraic discovery of the Pytha gorean triples as expressed by Bartel Leendert van der Waerden. It was used in megalithic monuments during that time which had right triangles with integers as its sides.

There were also written accounts during 2000 and 1786 BC which includes an Egyptian papyrus bearing a Pythagorean triple solution.

During the circa 1750 and 1790 BC, a Mesopotamian tablet also contained many written entries which were similar to Pythagorean triples during Hammurabi the Great’s reign.

India also had some records on the Pythagorean triples during the 2nd century and the 8th century BC.

That was years before Pythagoras (circa 580 BC to 500 BC) was said to have discovered this theorem. But, it was actually five centuries later after Pythagoras lived that the Pythagorean Theorem was attributed to Pythagoras.

The Tale of the Discovery of Pythagoras

It was believed that Pythagoras discovered this theorem when waiting for the tyrannical ruler, Polycrates. While looking at the floor’s square tiling of the palace of Polycrates, Pythagoras thought of this interesting idea: A diagonal line may be used to cut or divide the square, and two right triangles would be produced from the cut sides.

Examining it further, Pythagoras formulated the formula in mind.

A Modern Book Bearing the Answer

A book titled “The History of Mathematics” was written by Roger Cooke. In the pages of the book, Cooke shows that the Babylonians after all may have discovered the theorem years after the discovery of Pythagoras.

To support this belief, Cooke based it on Plato’s dialogue Meno. Cooke’s suggestions depict that the discovery may have been done as an element of fun or practical purpose by someone. And that someone may have thought it as necessary to make a square twice the size of a given square. To do so would result to about four right triangles with sides equal to the center square. It also can show two rectangles equal to the four triangles, and two squares on the bottom or legs of the right triangle. All these things point to the Pythagorean Theorem.

But with all these accounts, the Pythagorean Theorem is still linked to Pythagoras, the one believed by many to be the person who discovered the Pythagorean Theorem. Perhaps, it may be safe to say that although Pythagoras wasn’t the first to discover this, records show that this person may have been the first to prove this theorem.

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Most of us are familiar with the pi. Why wouldn’t we be when it is a staple of the basic math education that we get in high school? But it is safe to assume that most of us are not aware of some important facts about the pi. Familiar as the pi may be to us, questions such as ‘who discovered pi’, ‘how was the value acquired’, ‘why is it a constant’, will leave most of us dumbfounded. Knowing these facts may not be that essential for our everyday living but it won’t hurt as well especially given the fact that the pi is one of the elements that constitute the foundations of mathematics, and therefore of the modern world as well.

Before we go into answering who discovered pi, let’s first tackle a little bit of historical background relevant to its discovery. As early as 1900 BC, geometers from ancient civilizations such as Babylon, India, and Egypt, are already aware of one fundamental property of the circle: that a circle’s circumference is always a little over three times that of its diameter. A more precise value was not available however as each of the civilizations computed pi only within 1% of its actual value.

The individual who can then be said as the one who discovered pi is Archimedes since he is the first one to compute the value of the pi quite accurately. The man who discovered pi did so by comparing the perimeters of two polygons inscribed in a single circle; one is outside the circle and the other inside. The ratio of the bigger polygon’s perimeter with the smaller one’s will then be equivalent to the one between a circle’s circumference and its diameter. Archimedes did this technique to a total of 96 polygons and he got the average ratio, which is 3.14185. The value may not be spot on and only correct up to two decimal places but it is an improvement nonetheless over the computed values that the civilizations before him came up with.

Several individuals followed after Archimedes’ efforts to come up with the value of pi. Mathematicians such as Madhava, Al Kashi, and Ceulen, can be credited as much as Archimedes as people who discovered pi. With each of the said mathematicians computing pi up to tens of decimal places, great strides were made in the quest for the value of the pi.

The men who discovered pi did not only help in pioneering the quest to come up with the correct value of the pi, they contributed greatly to the development of mathematics, whose centrality in modern life will be impossible without the pi.

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The word  zero is attributed to many ancient cultures and is most likely a corrupt version of the Arabic spelling safira which meant it was empty. Coming down from the French cipher and zero, it finally became the word zero. The invention of zero as a number and not just for place position is generally attributed to the ancient Indians. By the 9^th century AD, mathematics calculations that included both division and multiplication used the number zero.  Pingala, who was an Indian scholar, also used zero for binary numbers, which was quite similar to Morse code.

The rules for using zero are now credited with Brahmagupta who was also an ancient Indian Scholar. The book treatise that he wrote known as “Brahmaputra Sidhantha” which translates to ‘The opening of the Universe. This treatise was written in 628AD. Along with rules for zero, the great scholar and mathematician had also laid down rules for negative numbers and algebra.

By the 6^th Century, zero was being used as a means to signify a position. The earliest mention of this arrangement has been discovered in the texts ‘Lokavibhaga’ which dates back to the 5^th century. By the 11^th century, the concept of using zero in the decimal system which used the base 10 finally reached the shores of Europe. This was brought to the European continent by Spanish Muslims, known as the Moors who also bought their knowledge of astronomy and this is the reason, that they are referred as the Arabic numerals. Fibonacci was really instrumental in using the system in Europe and using it for common mathematic problem solving.

Zero now plays a significant role in computing and also other streams of sciences where it can have special significance.

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The number system is extremely old and has been expressed in many ancient cultures for practical uses. Currently the most popular type of number system that is prevalent today is known as the Hindu Arabic numerals. The number system notation development is credited to two great mathematicians from ancient India, Aryabhat (5^th century BC) and Brahmagupta (6^th century BC). The simplest number system where even number is represented by marks is known as the unary numeral system. Here each and every natural number is represented by the number of corresponding marks, much like the tally marks that are still in use. This system is still used for teaching theories in computer science and can be used in practical use, but for smaller numbers only.

The ancient Egyptians and Romans modified this concept and laid down their own numerical system for various practical purposes. Many others like the Mayan system used the base 20 system. The place value system of numbers that has a base of ten uses 10 digits from 0 – 9 for making the positional numeral system work. This system makes it easier for working in arithmetic rather than other numeral systems. For the purpose of computer science, a modified k positional system is used, which is known as bijective numeration.

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Tags: Mathematics, Science