The history and features of analytic geometry

Following his lead, Pascal made his surprising discovery that the intersections of the three pairs of opposite sides of a hexagon inscribed in a conic lie on a straight line. The Islamic world improved the astrolabe as an aid for determining the time for prayers, for finding the direction to Mecca, and for astrological divination.

Any two points can be joined by a straight line. Archimedes also came West in the 12th century, in Latin translations from Greek and Arabic sources. Hobson, Ernest William 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.

Epistemology The application of geometry to astronomy reframed the perennial Greek pursuit of the nature of truth. Quadrature of the Lune.

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.

Although the treatment is excellent, it seems to me that the subject of this book is a relatively dry, light-weight part of mathematics from the modern point of view, unlike the much more satisfying history of calculus, " The History of the Calculus and Its Conceptual Development ", by the same author.

Dover, New York, Cavalieri's principleBonaventura Cavalieri observed that figures solids of equal height and in which all corresponding cross sections match in length area are of equal area volume.

The Bakhshali manuscript also "employs a decimal place value system with a dot for zero. As for the acute angle, Saccheri could defeat it only by appealing to an arbitrary hypothesis about the behaviour of lines at infinity.

All right angles are equal to each other. If two straight lines in a plane are crossed by another straight line called the transversaland the interior angles between the two lines and the transversal lying on one side of the transversal add up to less than two right angles, then on that side of the transversal, the two lines extended will intersect also called the parallel postulate.

Plato developed a similar view, and philosophers influenced by Pythagoras or Plato often wrote ecstatically about geometry as the key to the interpretation of the universe. Thus they assigned to the Sun a circle eccentric to the Earth to account for the unequal lengths of the seasons.

He was a competent geometer, but more importantly, he was a superb commentator on the works that preceded him. Although not published in his lifetime, a manuscript form of Ad locos planos et solidos isagoge Introduction to Plane and Solid Loci was circulating in Paris injust prior to the publication of Descartes' Discourse.

Thus he could compute the solar distance in terms of the lunar distance and thence the terrestrial radius. Doubling the cube The Vedic scriptures made the cube the most advisable form of altar for anyone who wanted to supplicate in the same place twice.Analytic geometry is widely used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight.

It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry.

Non-Euclidean geometry

History of Geometry See also history of Greek mathematics. On the Web. Xah Lee's A Visual Dictionary of Special Plane Curves. A list of articles on the history of geometry that have appeard in Math.

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History of analytic geometry. Scripta Mathematica, New York, Braummühl, Anton von. analytic geometry, branch of geometry in which points are represented with respect to a coordinate system, such as Cartesian coordinates, and in which the approach to geometric problems is primarily algebraic.

Its most common application is in the representation of equations involving two or three variables as curves in two or three dimensions or surfaces in three dimensions.

A History of Mathematics, 3rd Edition

Find helpful customer reviews and review ratings for History of Analytic Geometry (Dover Books on Mathematics) at Read. In the early 17th century, there were two important developments in geometry.

The first and most important was the creation of analytic geometry, or geometry with coordinates and equations, by René Descartes (–) and Pierre de Fermat (–). Analytic Geometry Analytic Geometry is the second course in a sequence of three high school courses designed to ensure career and college readiness.

The course embodies a discrete study of geometry analyzed by means of algebraic.

The history and features of analytic geometry
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