# The history and features of analytic geometry

After Archimedes, Hellenistic mathematics began to decline. Ancient Greece[ edit ] The Greek mathematician Menaechmus solved problems and proved theorems by using a method that had a strong resemblance to the use of coordinates and it has sometimes been maintained that he had introduced analytic geometry.

Thales is credited with bringing the science of geometry from Egypt to Greece. Let the sides sought for the rectangle be denoted by a and b. As for the acute angle, Saccheri could defeat it only by appealing to an arbitrary hypothesis about the behaviour of lines at infinity.

Stackel, Paul,editor. History of geometry The earliest known unambiguous examples of written records—dating from Egypt and Mesopotamia about bce—demonstrate that ancient peoples had already begun to devise mathematical rules and techniques useful for surveying land areas, constructing buildings, and measuring storage containers. A circle can be drawn with any center and any radius. Thus ancient geometry gained an association with the sublime to complement its earthy origins and its reputation as the exemplar of precise reasoning.

In three dimensions, a single equation usually gives a surfaceand a curve must be specified as the intersection of two surfaces see belowor as a system of parametric equations. Chelsea, New York, A comparison of a Chinese and a Greek geometric theoremThe figure illustrates the equivalence of the Chinese complementary rectangles theorem and the Greek similar triangles theorem.

Cartesian coordinate system The most common coordinate system to use is the Cartesian coordinate systemwhere each point has an x-coordinate representing its horizontal position, and a y-coordinate representing its vertical position. But the "real number line" is taught at a very early age in the schools now as if it were obvious.

The equation will be of the form As scaling all six constants yields the same locus of zeros, one can consider conics as points in the five-dimensional projective space The conic sections described by this equation can be classified using the discriminant  If the conic is non-degenerate, then: He found them in the only three-dimensional structures whose faces are equal regular polygons that meet one another at equal solid angles: That is, equations were determined by curves, but curves were not determined by equations. The evidence for that destruction is the most definitive and secure. Much less is known about Euclidhowever, than about Moses. The five Platonic solidsThese are the only geometric solids whose faces are composed of regular, identical polygons.

Non-Euclidian geometry generally refers to any geometry not based on the postulates of Euclid, including geometries for which the parallel postulate is not satisfied. Stevin, about AD, said that anything which can be achieved with geometry can be done in arithmetic. Polar coordinates in a plane [ edit ] Main article: Coordinates, variables, and equations were subsidiary notions applied to a specific geometric situation.

Geometry was too prolific of alternatives to disclose the true principles of nature.Analytic geometry was brought fourth by the famous French mathematician Rene' Descartes in Descartes did not start his studying and working with geometry until after he had retired out of the army and settled down.

Jan 11,  · The updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with Format: Paperback.

Analytic geometry. Analytic geometry was initiated by the French mathematician René Descartes (–), who introduced rectangular coordinates to locate points and to enable lines and curves to be represented with algebraic equations.

Algebraic geometry is a modern extension of the subject to multidimensional and non-Euclidean spaces. This Dover book, "History of Analytic Geometry" by Carl B. Boyer, is a very competent history of the way in which geometry made many transitions from the Euclidean geometry of lines, circles and conics to the algebraic reformulations by Fermat and Descartes, finally to the arithmetization of geometry which we now take for granted/5(3).

MATH ♦ History of Mathematics ♦ Fall Ren´e Descartes and Analytic Geometry What is Analytic Geometry? • Ingredients: (Euclid’s)geometry,therealnum. This Dover book, "History of Analytic Geometry" by Carl B. Boyer, is a very competent history of the way in which geometry made many transitions from the Euclidean geometry of lines, circles and conics to the algebraic reformulations by Fermat and Descartes, finally to the arithmetization of geometry which we now take for granted. The history and features of analytic geometry
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