By John Tabak
Geometry, Revised version 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 in the course of the ecu Renaissance in addition to the numerous mathematical development in different components of the realm. It additionally discusses the analytic geometry of Ren Descartes and Pierre Fermat, the choice coordinate structures invented by way of 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 larger dimensional geometry and geometry that's intrinsic to surfaces. the idea of relativity is usually tested in nice aspect during this full-color source.
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Extra resources for Geometry: The Language of Space and Form (The History of Mathematics)
Example text
Proof from Elements, one of Line EB is called the transversal. the most famous of all ancient Angle ABE equals angle BEF. Greek mathematics texts. An especially elegant proof, it is a good example of purely geometric thinking, and it is only three sentences long. To appreciate the proof one must know the following two facts: FACT 1: We often describe a right angle as a 90° angle, but we could describe a right angle as the angle formed by two lines that meet perpendicularly. In the first case we describe an angle in terms of its measure.
As a consequence it is difficult to place Pappus’s work in a historical context. Most of the history is missing. That is one reason that his principal work, Collection, is important. Pappus’s Collection is the last of the extant great Greek mathematical treatises. The Collection consisted of eight volumes. The first volume and part of the second have been lost. In the remaining six and a half volumes Pappus describes many of the most important works in Greek mathematics. He writes about, among others, Euclid’s Elements, Archimedes’ On Spirals, Apollonius’s Conics, and the works of the Greek astronomer Ptolemy.
2. Angle ACB equals angle CBF. ) 3. The sum of the interior angles of the triangle, therefore, equals angle ABE plus angle ABC plus angle CBF. These angles taken together form the straight angle EBF. Notice again that this type of reasoning does not require a protractor; nor does it make use of any numbers or algebraic equations. 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.