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About Euclidean Geometry

    The word geometry comes from the Greek geometrein (geo meaning earth, and metrein meaning to measure); geometry was originally the science of measuring the land. Euclid was a disciple of the Platonic school and around 300 B.C. he produced the definitive treatment of geometry in his 13-volume Elements: Books I-IV, VII came from the Pythagoreans, Book VIII came from Archytas, Books V, VI, and XII came from Eudoxus, and Books X and XIII came from Theaetetus, and so in compiling his masterpiece Euclid built on the experiences and achievements of his predecessors. Some of Euclid's assumptions used in his proofs were not stated explicitly; for example, there is nothing in Euclid's postulates from which we can deduce that an angle bisector of a triangle will intersect the opposite side, and thus Euclid simply assumed the existence of the needed point. Even so, Euclid's geometry reigned supreme until the 19th century when the discovery of non-Euclidean geometry brought about a re-examination of the foundations of Euclidean geometry. The concepts of incidence (i.e. a point lies on a line), betweeness (i.e. a point is between two other points), and congruence (i.e. line segments are congruent) have been the main improvements in Euclidean geometry since Euclid's time. Several great mathematicians including Pasch, Peano, Pieri, Veblen, Forder, Robinson, Levi, Hilbert, Birkhoff, and MacLane, and several groups including the School Mathematics Study Group (SMSG) and the University of Chicago School Mathematics Project (UCSMP) have made stunning improvements in Euclidean geometry as a mathematical (axiomatic) system. Eventually there evolved a consensus that the validity of a geometric axiomatic system was dependent on the consistency, independence, and completeness of the axiom set on which it is built and not on a physical or biased rationale. What is astonishing is the number and variety of propositions that can be deduced from so few assumptions.

Geometry Books

Calculus (With Analytic Geometry)(8th edition) List Price: $209.95 Buy Used: $71.79 You Save: $138.16 (66%) New (56) Used (173) from $71.79Designed for the three-semester calculus course for math and science majors, Calculus continues to offer instructors and students new and innovative teaching and learning resources. This was the first (more)

The Misbehavior of Markets: A Fractal View of Financial Turbulence List Price: $17.95 Buy New: $16.99 You Save: $0.96 (5%) New (5) Used (4) from $7.48From the inventor/founder of fractal geometry, the award-winning book that turns modern financial theory on its head Mathematical superstar and inventor of fractal geometry, Benoit Mandelbrot, has spent (more)

The Fractal Geometry of Nature Buy New: $34.99 New (6) Used (15) from $27.90Clouds are not spheres, mountains are not cones, and lightening does not travel in a straight line. The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary (more)

The Golden Ratio: The Story of PHI, the World's Most Astonishing Number List Price: $14.95 Buy Used: $4.81 You Save: $10.14 (68%) New (40) Used (51) Collectible (1) from $4.81Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale (more)

Trigonometry (9th Edition) List Price: $138.67 Buy New: $85.32 You Save: $53.35 (38%) New (33) Used (29) from $85.32Over the years, the text has been shaped and adapted to meet the changing needs of both students and educators. As always, special care was taken to respond to the specific suggestions of users and reviewers (more)

Geometry List Price: $94.88 Buy Used: $6.95 You Save: $87.93 (93%) New (29) Used (117) from $6.95Geometry (more)

Geometry For Dummies (For Dummies (Math & Science)) List Price: $19.99 Buy New: $8.52 You Save: $11.47 (57%) New (53) Used (10) from $8.52Learning geometry doesn?t have to hurt. With a little bit of friendly guidance, it can even be fun! Geometry For Dummies, 2nd Edition, helps you make friends with lines, angles, theorems and postulates. (more)

College Algebra with Modeling and Visualization (3rd Edition) (Rockswold Series) List Price: $138.67 Buy Used: $20.00 You Save: $118.67 (86%) New (25) Used (127) from $20.00Gary Rockswold focuses on teaching algebra in context, answering the question, "Why am I learning this?" and ultimately motivating the students to succeed in this class. In addition, the author's understanding (more)

Euclid's Elements List Price: $29.95 Buy New: $25.99 You Save: $3.96 (13%) New (2) from $25.99Green Lion Press has prepared a new one-volume edition of T.L. Heath's translation of the thirteen books of Euclid's "Elements" In keeping with Green Lion's design commitment, diagrams have been placed (more)

The Symmetries of Things List Price: $75.00 Buy New: $60.00 You Save: $15.00 (20%) New (7) Used (4) from $59.99Start with a single shape. Repeat it in some way translation, reflection over a line, rotation around a point and you have created symmetry. Symmetry is a fundamental phenomenon in art, science, and nature (more)