In most mathematics textbooks, the most exciting part of mathematics - the process of invention and discovery - is completely hidden from the student. The aim of Knots and Surfaces is to change all that. Knots and Surfaces guides the reader through Euler's formula, one and two-sided surfaces, and knot theory using games and examples. By means of a series of carefully selected tasks, this book leads the reader on to discover some real mathematics. There are no formulas to memorize; no procedures to follow. This book is a guide to the mathematics - it starts you in the right direction and brings you back if you stray too far. Discovery is left to you. This book is aimed at undergraduates and those with little background knowledge of mathematics.A Guide to Discovering Mathematics David W. Farmer, Theodore B. Stanford. drawn on the torus, but the large outside region will not be a cell. ... Replace e by e + 2 and C by C + 2 in all of your formulas for the sphere, and you will wind up with v a e + f = 0 for the torus. Task 2.4.3: A torus can be built from a sphere by cutting out two triangles and gluing the cut edges together: Altogether the triangles had 6 ... So in going from a sphere to a torus we a#39;losta#39; 3 vertices, 3 edges , and 2 faces.

Title | : | Knots and Surfaces |

Author | : | David W. Farmer, Theodore B. Stanford |

Publisher | : | American Mathematical Soc. - |

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