This may be done by use of the more familiar Cartesian coordinates, by something such as polar coordinates or by just about any system for defining coordinates in a Euclidean space. The Common Core has the concept of graphing introduced in 5 th grade, and graphing simple functions in the 8 th grade.
Join Kobo & start eReading today
The earliest evidence of anything resembling analytic geometry was by the Geek mathematician Menaechmus — BC , who was a student of Eudoxus and a tutor of Alexander the Great. These were used along with something resembling analytic geometry to solve the Delian problem, which is to, given the edge of a cube to construct the edge of a cube with double the volume.
Though most of what we know of Menaechmus and his exact solution is second hand as his original work was lost, it appears as though he argued his solution for doubling the cube with proportions of a side length to the area of a side which fairly quickly leads to conics. He drew a connection between algebra and geometry in his solution of general cubic equations. His idea to do this was to create a geometrical construction of a cubic equation by considering the variable to be the edge of a cube and constructing a set of curves from which a solution could be discerned.
While it might seem far flung from Cartesian coordinates it was a significant leap in connecting the separate concepts of algebra and geometry. Descartes published first and so he is commonly credited as the sole creator which leads to analytic geometry often being call Cartesian geometry.
While the Fermat and Descartes constructions are equivalent, they did differ in several ways which primarily stem from which direction their creator worked. May 31, Sold by: Share your thoughts with other customers. Write a customer review. Showing of 3 reviews. Top Reviews Most recent Top Reviews. There was a problem filtering reviews right now. Please try again later.
- There was a problem providing the content you requested;
- History of Geometry.
- History: Source Books.
- My Joy In the Morning: Daily Prayer.
- The Devil Draws Two.
- Avocado Nutritional Value.
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. 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.
Perhaps the reason for this apparent shallowness of coordinate geometry is that it is now so totally accepted in modern life, for example in longitude and latitude for the Earth, X and Y coordinates for computer monitor pixels or printer dots, and for every graph we ever see during school education or working life.
Product Review
Therefore to appreciate this history by Boyer, one must try to imagine the mind-set of pure mathematicians from Euclid to Euler, who believed that numbers and magnitudes are fundamentally different. Even in Euler's relatively modern work, "Introductio in analysin infinitorum", numbers are referred to as "lines" in Latin , and this idea persisted well into the 19th century. Boyer points out on pages 92 and that it was only with the Cantor-Dedekind axiom that the identification of numbers with the points on a line is made explicit, late in the 19th century.
But the "real number line" is taught at a very early age in the schools now as if it were obvious. What has happened is that numbers have developed so as to "fill in the gaps" on the "real number line" with algebraic and transcendental numbers. We take for granted now that numbers include decimal expansions to any number of significant digits, even infinite, but this was not part of mathematical understanding until the 19th century. This book shows how geometry was gradually, and sometimes painfully, developed until the algebraic and numerical viewpoints prevailed.
Some of the points in this book which I have added marginal notes for are as follows. It was Plato who required geometry to be concerned only with ruler and compass, not Euclid. According to Proclus and Eutocius, it was Menaechmus who discovered the 3 kinds of conics about BC. It was Apollonius who gave the names to the ellipse, parabola and hyperbola. Originally, cubic and quartic equations were solved using the geometry of conics, but from about onwards, there were algebraic methods to achieve the same objective.
Stevin, about AD, said that anything which can be achieved with geometry can be done in arithmetic. Wallis, about , introduced negative abscissas X coordinates , but "the significance of this step was not appreciated by his contemporaries".
- Seduced By His Touch (Byrons of Braebourne).
- History of Analytic Geometry (Dover Books on Mathematics) Unabridged, Carl B. Boyer - tandjfoods.com;
- A DEVIL IN THE CITY OF ANGELS;
- Goliath Gets Up.
- History of Math References.
Jean Bernoulli in was the first to use the term "Cartesian geometry" for geometry based on a coordinate system. Clairaut in defined the distance between two points in 2 and 3 dimensional coordinate space as the square root of the sum of the squares of the coordinate differences.
History of Analytic Geometry - Carl B. Boyer - Google Книги
Throughout the book, Boyer discusses the fundamental question of what distinguishes "analytic geometry" from the earlier geometry, whether it is the use of coordinates, the application of algebra or arithmetic to geometry, or the application of geometry to algebra or arithmetic, or maybe something else. Perhaps this is the weak point of the book. It is not really clearly stated what "analytic geometry" means. So it's difficult to know when it started, and which topics belong to calculus rather than analytic geometry.
Covers the subject neatly and rigorously. Good writer, has the rare skill of getting mathematics concepts across cleanly. Everyone I show this book to wants their own copy. So I give them mine and get another. Analytic geometry is where the maths student first encounters the combining of traditional Euclidean geometry with algebra.
A profound mix, though perhaps most students won't appreciate it as such.
Boyer shows how, slowly, the necessary ideas in analytic geometry came together. He traces the first stirrings back to the classical era of ancient Greece and Rome. But the greatest step may well have been due to Rene Decartes and his laying down of the x and y grid in two dimensions. Plus, of course, analytic geometry was necessary for the development of calculus, with the concept of a slope. You probably are already familiar with all of the maths that the book covers. What Boyer offers is an appreciation of the great minds that preceded up and made these achievements.