## Mathematical Byways in Ayling, Beeling and CeilingUnique and highly original, Mathematical Byways is a work of recreational mathematics, a collection of ingenious problems, their even more ingenious solutions, and extensions of the problems--left unsolved here--to further stretch the mind of the reader. The problems are set within the framework of three villages--Ayling, Beeling, and Ceiling--their inhabitants, and the relationships (spacial and social) between them. The problems can be solved with little formal mathematical knowledge, although most require considerable thought and mental dexterity, and solutions are all clearly expounded in non-technical language. Stimulating and unusual, this book proves what Hugh ApSimon has known all along: mathematics can be fun! |

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### Contents

Introduction | 1 |

Complete quadrilateral | 13 |

Bowling averages | 19 |

Copyright | |

7 other sections not shown

### Common terms and phrases

AAOP ABOQ angle AOPQ AOPR AOQR APQR Ayling Arms boundary of FGH Bowling averages Circle circumcircle Complete quadrilateral Composer's problem coprime correct material cyclic quadrilateral destination Diagram Dick equations equilateral five mints five segments Harry Hence highest common factor integer solution integer values involve ladder last possible least left-hand-side length line-segments Mathematical Byways minimum network consists minutes multiple intersection normal wrapping number of coins opposite parity particular problem set Particular solution prevent the sheep's Pythagorean triplets quadrangle quadratic quadratic equation quartic quartic equation Quince rectangular sheets restraint runs scored scooter sheep runs sheep-dog trials sheep's escaping sheep's path sides size zero skew-rectangular wrapping solve solver speed square miles square yards steeply than 45 Table theorem three mints travel on foot Treasury Uncle Timothy variant material vehicle usage wall weigh Wickets wild point wrapper wrapping paper zero