Ancient Egyptians demonstrated a practical knowledge of geometry through surveying and construction projects. The Nile River overflowed its banks every year, and the river banks would have to be re-surveyed.
Ancient clay tablets reveal that the Babylonians knew the Pythagorean relationships. The Babylonians also used degree measurements for angles. The Babylonian numerals were based on the number 60, and 60 degrees could have come from the radius of a circle.
Thales was credited as the first person to use deductive math reasoning. He calculated the distance from a ship, to the shore and measured the height of pyramids. His theorem says that if AC is the diameter, than angle ABC is a right angle.
Pythagoras was one of the most famous ancient Greek philosophers. He was credited for creating the Pythagorean theorem (a2 + b2 = c2).
Plato was a Greek philosopher and mathematician. He was Plato's sophistication as a writer is evident in his Socratic dialogues; thirty-six dialogues and thirteen letters have been ascribed to him. Plato's writings have been published in several fashions; this has led to several conventions regarding the naming and referencing of Plato's texts. Plato's dialogues have been used to teach a range of subjects, including philosophy, logic, ethics, rhetoric, and mathematics. Plato is one of the most important founding figures in Western philosophy (Wiki).
important geometry book, Euclid’s Elements, studied and created by Euclid, formed the basis for most of the geometry studied in schools everywhere.
Archimedes was a Greek mathematician, physicist, engineer, inventor, and astronomer. He was credited for inventing the Archimedes screw, and the method of exhaustion, which analyzes the area under the arc of a parabola with summing up on a never-ending series, and gave a remarkably accurate approximation of pi.
Apollonius of Perga was a Greek geometer and astronomer who was credited with giving the ellipse, the parabola, and the hyperbola the names by which we know them. The hypothesis of eccentric orbits, or equivalently, deferent epicycles, to explain the apparent motion of the planets and the varying speed of the Moon, is also attributed to him.
Euler was a Swiss mathematician credited with finding the Euler line.
Since mathematicians couldn't prove the 5th postulate; they devised new geometries with "strange" notions of parallelism. (Geometry with no parallel lines) Bolyai and Lobachevsky are credited with devising the first Non-Euclidean types of geometry.
Fractals are geometric figures that model many natural structures like ferns or clouds. The invention of computers has greatly aided the study of fractals since many calculations are required.
M.C. Escher was famous for his so-called impossible structures. He was an architect that turned into a drawing artist.
Marjorie Rice is a American mathematician. She is most famous for her work with tessellations, and is known for tiling a plane using pentagons. She developed her own system to represent the restrictions and relationships between the sides and angles of the polygons. She used it to discover four new types of tessellating pentagons and over sixty distinct tessellations.
Sir Roger Penrose is a English mathematical physicist, philosopher, and professor of mathematics at the University of Oxford in England. He is internationally renowned for his scientific work in mathematical physics, in particular his contributions general relativity and cosmology. He generalized the matrix inverse, also known as the Moore-Penrose Inverse. He devised and popularized the Penrose triangle, describing it as "impossibility in its purest form" and exchanged material with the artist M. C. Escher, whose earlier depictions of impossible objects partly inspired it (Wiki).
Today, geometry that is taught at schools comes from what has been known for thousands of years. In geometry, new discoveries are being made every day, which will further our knowledge of it. We credit the geometry that is known today to all the mathematicians and geometers prior to us, for their extensive knowledge on the subject.