## Mathematical Adventures for Students and AmateursDavid F. Hayes, Tatiana Shubin, Gerald L. Alexanderson, Peter Ross This is a partial record of the Bay Area Math Adventures (BAMA), a lecture series for high school students (and incidentally their teachers, parents, and other interested adults) hosted by San Jose State and Santa Clara Universities in the San Francisco Bay Area. These lectures are aimed primarily at talented high school students and as a result, the mathematics in some cases is far from what one would expect to see in talks at this level. There are serious mathematical issues addressed here. The authors are distinguished mathematicians; some are bright newcomers while others have been well known in mathematical circles for decades. We hope that this book will capture some of the magic of these talks that have filled auditoriums at the host schools almost monthly for several years. Join the students in sharing these mathematical adventures. |

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### Contents

Prime Numbers and the Search for Extraterrestrial Intelligence | 3 |

Triangles Squares Oranges and Cuboids Peter Stevenhagen | 51 |

When Is an Integer the Product of Two and of Three Consecutive Integers? | 65 |

Right Triangles and Elliptic Curves Karl Rubin | 73 |

The Magic of Fibonacci Numbers and More | 83 |

The Rule of False Position Don Chakerian | 157 |

Geometric Puzzles and ConstructionsSix Classical Geometry Theorems | 169 |

Cusps Dmitry Fuchs | 185 |

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algebra Alice angle Archimedes balls braided model breakable Brianchon's Theorem called cells circle combinatorial conformal map congruent number corresponding counting the number cube cusps cylindrical projection defined density disk dodecahedron Dodgson domino edges elliptic curves entire function equation example Exercise faces Fibonacci Fibonacci numbers Figure finite formula fundamental group geodesic space geometry given harmonic numbers hexagon horizontal icosahedron identity infinity initial digits intersect juggling sequence length license numbers Liddell look Math mathematicians mathematics meromorphic function Mersenne prime metric space n-tiling nonpositive curvature nonpositively curved number theory octahedron odd numbers pairs parabola parallel Pascal's Theorem perfect number permutation Picard's Theorem plane Platonic Solids polynomial prime number problem proof Proposition prove rational points right triangle scale sides solution sphere square surface swap tangent tetrahedron tiling torus twin primes unbounded regions University values vertex vertical x-axis z-plane