PRINT LINKED RELATED

Saccheri-Legendre Theorem

    This topic defines a Dedekind cut and proves the Dedekind Axiom implies the Archimedian Axiom. After introducig the measure of a segment and an angle, the triangular inequality and the Saccheri-Legendre Theorem are proven.

Proposition (Saccheri-Legendre) The sum of the degree measures of the three angles of a triangle is less than or equal to

    Proof. Assume, on the contrary, that the angle sum of is greater than say where is a positive number. By the Equilvalent Angle Sum Proposition, replace with another traingle that has the same angle sum as but in which one of the angles has at most half the number of degrees as Repeat the procedure to get another triangle that has the same angle sum as   and has an angle that is one-quarter the degree measure of   The Archimedian Principle for real numbers guarantees that if this process is repeated enough times, eventually a triangle that has angle sum and with one angle with degree measure at most Thus, the sum of the degrees measures of the other two angles will be greater than or equal to contradicting the Two Angles In A Triangle Proposition.

Geometry Books

Calculus (With Analytic Geometry)(8th edition) List Price: $209.95 Buy Used: $69.00 You Save: $140.95 (67%) New (57) Used (180) from $69.00Designed 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: $16.15 You Save: $1.80 (10%) New (4) Used (5) from $7.47From 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: $4.83 You Save: $10.12 (68%) New (40) Used (50) Collectible (1) from $4.83Throughout 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)

Geometry For Dummies (For Dummies (Math & Science)) List Price: $19.99 Buy New: $8.62 You Save: $11.37 (57%) New (51) Used (10) from $8.62Learning 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)

Trigonometry (9th Edition) List Price: $138.67 Buy New: $85.49 You Save: $53.18 (38%) New (33) Used (33) from $85.49Over 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)

Baby Einstein: See and Spy Shapes List Price: $5.99 Buy Used: $0.01 You Save: $5.98 (100%) New (25) Used (97) Collectible (1) from $0.01Shapes invites babies and young children to identify different shapes in bold, graphic illustrations featuring the Baby Einstein characters. Playful poems will inspire children to seek out shapes in the (more)

Geometry List Price: $94.88 Buy Used: $6.95 You Save: $87.93 (93%) New (29) Used (122) from $6.95Geometry (more)

College Algebra with Modeling and Visualization (3rd Edition) (Rockswold Series) List Price: $138.67 Buy New: $20.00 You Save: $118.67 (86%) New (26) Used (129) from $19.99Gary 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: $24.45 You Save: $5.50 (18%) New (5) from $24.45Green 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)