Download e-book for kindle: Geometry: The Language of Space and Form (The History of by John Tabak

By John Tabak

ISBN-10: 0816079420

ISBN-13: 9780816079421

Geometry, Revised variation describes geometry in antiquity. starting with a quick description of a few of the geometry that preceded the geometry of the Greeks, it takes up the tale of geometry throughout the ecu Renaissance in addition to the numerous mathematical development in different parts of the realm. It additionally discusses the analytic geometry of Ren Descartes and Pierre Fermat, the choice coordinate structures invented through Isaac Newton, and the forged geometry of Leonhard Euler. additionally incorporated is an outline of the geometry of 1 of the main profitable mathematicians of the nineteenth century, Bernhard Riemann, who created either better dimensional geometry and geometry that's intrinsic to surfaces. the idea of relativity can be tested in nice element during this full-color source.

Show description

Read or Download Geometry: The Language of Space and Form (The History of Mathematics) PDF

Best mathematics books

Download e-book for kindle: What Is Mathematics? An Elementary Approach to Ideas and by Richard Courant, Herbert Robbins

"A lucid illustration of the elemental recommendations and strategies of the total box of arithmetic. it's an simply comprehensible creation for the layman and is helping to provide the mathematical pupil a common view of the elemental rules and strategies. "--Albert Einstein (on the 1st version)
For greater than thousand years a familiarity with arithmetic has been considered as an integral a part of the highbrow gear of each cultured individual. this day, regrettably, the conventional position of arithmetic in schooling is in grave chance. The instructing and studying of arithmetic has degenerated into the area of rote memorization, the result of which ends up in passable formal skill yet to not actual knowing or larger highbrow independence. This new version of Richard Courant's and Herbert Robbins's vintage paintings seeks to handle this challenge. Its aim is to place the which means again into arithmetic.
Written for rookies and students, for college students and academics, for philosophers and engineers, what's arithmetic? , moment version is a gleaming choice of mathematical gemstones that gives an unique and obtainable portrait of the mathematical international. masking every thing from usual numbers and the quantity process to geometrical structures and projective geometry, from topology and calculus to concerns of precept and the Continuum speculation, this interesting survey permits readers to delve into arithmetic as an natural entire instead of an empty drill in challenge fixing. With chapters mostly autonomous of each other and sections that lead upward from simple to extra complicated discussions, readers can simply decide and select components of specific curiosity with out impairing their knowing of next elements. stated thus far with a brand new bankruptcy through Ian Stewart, what's arithmetic, moment version deals new insights into fresh mathematical advancements and describes proofs of the Four-Color Theorem and Fermat's final Theorem, difficulties that have been nonetheless open whilst Courant and Robbins wrote this masterpiece, yet ones that experience in view that been solved.
Formal arithmetic is like spelling and grammar: a question of the right kind software of neighborhood ideas. significant arithmetic is like journalism: it tells an attractive tale. yet in contrast to a few journalism, the tale should be actual. the simplest arithmetic is like literature: it brings a narrative to existence ahead of your eyes and consists of you in it, intellectually and emotionally. what's arithmetic is a marvelously literate tale: it opens a window onto the realm of arithmetic for an individual to view.

Ilja N. Bronshtein, Konstantin A. Semendyayev, Gerhard's Handbook of Mathematics PDF

This consultant ebook to arithmetic comprises in guide shape the basic operating wisdom of arithmetic that is wanted as a regular consultant for operating scientists and engineers, in addition to for college students. effortless to appreciate, and handy to exploit, this consultant e-book supplies concisely the knowledge essential to review so much difficulties which take place in concrete purposes.

Additional info for Geometry: The Language of Space and Form (The History of Mathematics)

Sample text

In the first case we describe an angle in terms of its measure. In the second case we describe a right angle in terms of the way it is formed. The descriptions are equivalent, but the Greeks used only the latter. With this description the Greeks described a straight (180°) angle as the sum of two right angles. FACT 2: When we cut two parallel lines with a third, transverse line, the interior angles on opposite sides of the transverse line are equal. ) Notice that no measurement is involved. We can Early Greek Geometry 11 a circle and one of its diameters makes it clear that the diameter bisects the circle.

He restored it. In addition to his work on three-dimensional forms, Archimedes studied curves. He wrote an entire treatise entitled On Spirals. Here is how he described the spiral: If a straight line drawn in a plane revolve at a uniform rate about one extremity which remains fixed and return to the position from which it started, and if, at the same time as the line revolves, a point move at a uniform rate along the straight line 32 GEOMETRY beginning from the extremity which remains fixed, the point will describe a spiral in the plane.

It is pure geometrical reasoning, the type of reasoning at which the Greeks excelled. indd 11 3/7/11 11:40 AM 12 GEOMETRY the ­importance of deductive reasoning. Deductive reasoning, the process of reasoning from general principles to specific instances, is the characteristic that makes mathematics special. Mathematics is a deductive discipline. All mathematicians today work by beginning with known principles and then deriving new facts as logical consequences of those principles, but Thales was the first to apply this method rigorously.

Download PDF sample

Geometry: The Language of Space and Form (The History of Mathematics) by John Tabak

by Robert

Rated 4.53 of 5 – based on 13 votes