What is Geometry?
What is Geometry? Even though geometry is a subject area originated from the mathematics studies, it is undoubtedly one of the most fundamental areas of research serving to solve everyday problems of humanity and explain the way our world works.
Geometry is a subject area that is concerned with sizes, shapes, positions angles and dimensions of things. Thus, we can find geometry in every corner of our lives. In fact, the rise of geometry starts with philosophers and thinkers observing the nature and things around them. One of the most fascinating and deep-rooted practices of the world. If you think that geometry is just a challenging topic at school you might want to dive into its rich history.
This elegant practice originates from the concerns of everyday life and has a long past starting from 3100 BCE in Egypt and Mesopotamia.
Origins of Geometry
The greatest minds of the time planted the origins of geometry to try and solve the problems with land sharing, building, and measuring storage areas. But geometry, as we know it today, has risen in the 6th century BCE and owes its evolution to the great Greek philosophers such as Aristotle, Euclid, Plato, and many others. Greek philosophers are also the ones to coin the word “geometry” which is essentially the combination of the Greek words geo (“Earth”) and metron (“measure”).
Greek Influence on Geometry
Geometry has found solid ground with the influence of Greek logic and philosophy. Starting from Thales, Greek philosophers have created different ways of thinking that have act as the basis for geometry.
Thales of Miletus
Thales of Miletus is the first person known to practice scientific philosophy. He used geometry to calculate the height of the Egyptian Pyramids and long distances. Thales is also the first person to be attributed a mathematical discovery with the Thales’ Theorem.
Then comes Pythagoras to leave his stamp on geometry and mathematics. Considered as one of the most important Greek philosophers, he influenced many other philosophers such as Plato and latemathematicians. Pythagoras has left behind the Pythagorean theorem and the theory of proportions which are the cornerstone of geometry even in the 21st century.
Plato, who is known as the “maker of mathematicians” has not only contributed to the rise of geometry but also educated numerous valuable geometers and mathematicians. He is known for the identification of 5 regular symmetrical 3-dimensional shapes, which he considered as the basis for the whole universe. These geometric shapes known as platonic solids are tetrahedron, octahedron, icosahedron, cube, and dodecahedron. For Plato, each of these shapes represents different elements such as fire, air, water, and earth while the dodecahedron represents the harmony of constellations. At Plato’s door, “Non-geometricians cannot enter our house!” the inscription is transmitted.
Euclid followed the steps of Aristotle in scientific philosophy and affected the world of mathematics and geometry irrefutably. His influential work “elements of mathematics” was the basis of numerous geometrical theorems and ideas. In this work, Euclid created a series of definitions of basic objects like points, straight lines, parallel lines surfaces, angles, circles and triangles, andaxioms. The Euclidean geometry we know today is based on these definitions and postulated derived from them. This is why Euclid’s influence on geometry is indisputable.
We can’t talk about geometry without mentioning Archimedes. Considered as one of the greatest Greek mathematicians, Archimedes has contributed a great deal to the evolution of geometry. He was the one to discover the formula for how to calculate the volume of a cylinder and prove many other geometrical theories.
Eastern Influence on Geometry
Several Eastern thinkers followed and criticized the work of Euclid and contributed to the new areas of geometry. Abul Wafa al-Buzjani, Omar Khayyam, Nasir al-Din al-Tusi, and many others showed great works on geometry.
Abul Wafa al-Buzjani
Abul Wafa is very well-known for his work on trigonometry. Working on understanding the Moon’s orbit, he wrote “theories of the Moon” which included valuable information such as the first introduction of the tangent, secant,and cosecant functions and improvement in calculations for trigonometrical tables. For his valuable contributions, a crater on the Moon is named after Abul Wafa. His work on spherical triangles is also one of his most important contributions to geometry.
Abul Wafa al-Omar Khayyam
Omar Khayyam is one of the most influential Islamic mathematicians. His work on the geometrical method of solving cubic equations by intersecting a parabola with a circle has created great attention. In addition, he discovered some non-Euclidian properties while looking to prove Euclid’s fifth postulate. He is also well-known for constructing the quadrilateral with two equal sides perpendicular to the base.
What is Modern Geometry?
The works of European geometers are known as modern geometry. Some of the most important figures of modern geometry are Descartes, Gauss, Newton, Riemann, and Leibniz. Geometers of the modern age have dealt with non-euclidian geometry. Analytic geometry which uses algebra to represent and solve problems in geometry was first initiated by the French mathematician Rene Descartes in hopes to understand the non-Euclidian spaces.
Another important product of modern geometry is the development of differential geometry which deals with properties of curves and surfaces using differential calculus.
Ultimately, geometry is an elegant practice standing upon a philosophical foundation, shining a light upon the day-to-day problems, and helping us understand the mysterious ways of the World.