Written by Yamini Bharadwaj, a grade 9 student.
For most of us, mathematics is almost inseparably associated with never-ending pages of homework and the thin, groaningly tick-marked and dog-eared pages of bulky textbooks. Often overlooked at school is this mysterious and intriguing underside to math which makes it slightly more enjoyable – the history that is behind it.
Elements of Geometry
Euclid (c. 325 to c. 265 BCE) was one of the most prominent mathematicians of Greco-Roman antiquity and is known as the ‘Father of Geometry’. He wrote The Elements of Geometry which was used as a maths textbook in Europe and the Middle East for two-thousand years!
His treatise on geometry contained definitions, proofs, axioms, theories, the golden ratio, and practical applications of mathematics. The geometry we study today at school – the type that deals with points, lines, planes, and other figures are part of Euclidean geometry.
From various Greek records, the stories of Euclid have been extrapolated which shines a light on the kind of man and mathematician he was. Once, Ptolemy, pharaoh of Egypt asked Euclid, “Is there any shortcut for me to take in geometry?” To which Euclid replied, “Geometry only has one road. There is no royal road.”
Eureka and Mechanical Mathematics
Archimedes of Syracuse was the most well-known Greek mathematician and inventor, credited for the invention of the water pump, compound pulley, and the popularisation of “Eureka!”
The king of Syracuse, Hieron, had asked Archimedes to prove whether or not the crown he wore was made of pure gold as the goldsmith claimed. Archimedes was lost as to how he could prove such a thing, and deeply brainstormed away. One day, he had filled his tub with water for a bath and when he entered it, he realised that the amount of water displaced was equal to the weight of the body which displaced it. He knew that gold was heavier than other metals which could be substituted. He had his solution, and ran naked around the streets of Syracuse elated and shouting, “Eureka!” or in English, “I have it!” This was the birth of Archimedes’ Principle of buoyancy.
Perhaps it was in ancient Babylon, four thousand years ago that we were introduced to the mysterious number pi. William L. Schaff said about it, “Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception, and human interest as the number pi.” No one person calculated pi first, rather it was discovered independently in nearly all ancient civilisations. However, it was Zu Chongzhi (429-500 CE) who was the first person to calculate the symbol to seven decimal places between 3.1415926 and 3.1415927 correctly. He obtained the result by approximating a circle with a 24,576 sided polygon [I.e (2^13)*3-sided]! Such accuracy was only replicated in Europe several thousand years later.
Sick in bed and perhaps intolerably bored, René Descartes observed a fly present on his ceiling and wondered how he could explain its exact location of it. He realised he could detail its location by stating its difference from the walls. He had invented the coordinate plane! The fly’s progression could be geometrically represented by the line of its path and the shapes created by the line, and algebraically expressed using a series of points. Whether this story of the fly is fact or fiction matters no more since we know who to blame for the puzzling questions on graphs and equations.
His contribution to analytical geometry linked algebra and geometry and inspired the discovery of calculus by Isaac Newton. Descartes was also the one to introduce superscripts to indicate exponents.
Algebra can be traced back to the ancient Middle East, Greece, and the Renaissance. The word itself is derived from the Arabic word ‘Al-jabr’ which comes from a treatise written on the subject by the Persian mathematician, Muhammad ibn Musa Al Khwarizmi in 820 AD.
The Rhind papyrus (c. 1650 BC) and other ancient texts prove the ability of Egyptians to solve linear equations, problems involving a system of two equations, and quadratic equations. In all these problems, symbols were not used, rather they were solved verbally.
Many Babylonian tablets also contained problems seeking the solution to an unknown number. These questions were mostly application-based, discussing the partition of fields amongst brothers and other situations along these lines.
In Greek, we say hello to Euclid again, this time with Diophantus and Pythagoras. In his Pythagorean theorem, Pythagorus relates the diagonal of a right-angled triangle with its two other sides using variables. The geometric constructions that appear in Euclid’s Elements of Geometry are translated into modern algebraic language and establish algebraic identities, solve quadratic equations, and produce related results despite never having employed any symbols. It was Diophantus (c. 250. AD) who introduced some sort of symbolism for polynomial equations in Greek. However, Diophantus could not believe any problems resulting in a negative number and called them ‘absurd’.
In India, mathematicians like Brahmagupta (598-670 AD) and Bhaskara II (1114-1185 AD) developed very precise procedures for solving first and second-degree equations and equations in more than one variable. However, they too did not use symbols. Yet, consistent and correct rules for operating with not only positive but also negative numbers and zero were developed.
From years of research and interesting circumstances, the mathematics we know today has sprung. It would not exist without people passionately and intently working on the subject, and shedding light on our understanding of the theoretical and practical world.
By Yamini Bharadwaj
Yamini is an artist and a writer. She loves to paint in her free time