## Archive for geometry

You are browsing the archives of geometry.

You are browsing the archives of geometry.

In 1872, Felix Klein, at the age of 23, having just been appointed as a professor at the University of Erlangen in Germany, published a manifesto that described a new direction for geometry. Klein was attempting to unify classical Euclidean geometry with the new non-Euclidean geometries and some elements of topology by showing that some […]

Group theory is about groups of objects that have similar characteristics. Objects can show different kinds of symmetry when they are transformed by a standard set of operations. A basic transformation operation is turning (called rotation in the world of symmetry). When an object is rotated, depending upon the shape of the object and the […]

Baudhayana lived some time around -0800 in India and contributed to appendices of the Vedic hymns known as Shulba Sutras. The Shulba Sutras were instructions on the design and construction of fire altars and contained geometric principles including the Pythagorean theorem and rules for constructing many geometric shapes. They included Pythagorean triples, calculations using decimals […]

Nikolai Ivanovich Lobachevsky was born in 1792 in Russia and became a mathematician known for developing non-euclidian geometry. He also found a method for approximating roots of algebraic equations that is now known as the Dandelin-Graffe method. Lobachevsky, Bolyai and Gauss all appear to have independently discovered the form of non-euclidean geometry called hyperbolic geometry […]

Georg Friedrich Bernhard Riemann was born in 1826 in Breselenz, Germany. He worked on analytic geometry, algebraic geometry, and both non-euclidean and n-dimensional geometries. Some of this work laid important foundations for Einstein’s theory of relativity. He composed the famous “Riemann Hypothesis” which deals with predicting prime numbers. He was a student under Gauss. PRECURSOR: […]

Anaximander was a Greek philosopher who studied under Thales and taught Pythagoras. He studied geometry and geography and may have been the first to draw a map of the world. He created a mechanical model of the universe that had Earth at its center. He attempted to explain phenomena such as lightning and thunder by […]

pi or π is a constant but irrational number that represents the ratio between the area of any circle and the square of its radius. This gives us the famous formula: area = π x r2, which can be approximated by 22/7 or 3.14159. pi can also be expressed by dividing the circumference of any […]

Felix Christian Klein was born in Dusseldorf, Germany and was a mathematician. He did work on group theory and non-Euclidian geometry. He wrote a book on the icosahedron and created a 4-dimensional construct that is known as the “klein bottle”. PRECURSOR: Plucker 1826 – Riemann CONCURRENT: 1842 – Lie 1844 – Boltzmann 1854 – Poincare […]

Lobachevsky becomes the first to publish a theory of non-Euclidean geometry even though Gauss had worked on the same ideas earlier and Bolyai was working on it concurrently although independently of Lobachevsky. Bolyai published in 1832. Riemann and Klein advanced the work later. Euclid’s “The Elements” contained postulates and axioms of geometry that set the […]