Mathematics Through Paper Folding

# Mathematics Through Paper Folding - MATHEMATICS T HROUGH...

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MATHEMATICS THROUGH PAPER FOLDING Alton T. Olson INDIA N EDITIO N BY Mathematical Sciences Trust Society

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Mathematics through Paper Folding ALTON T. OLSON University of Alberta Edmonton, Alberta NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS MATHEMATICAL ASSOCIATION OF INDIA

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Copyright © 1976 by THE NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS, INC. 1906 Association Drive, Reston, Virginia 22091 All rights reserved Sixth printing 1989 Library of Congress Cataloging in Publication Data: Olson, Alton T Mathematics through paper folding. Bibliography: p. 1. Mathematics—Study and teaching—Audio-visual aids. 2. Paperwork. I. Title. QA19.P34038 516'.2 75-16115 ISBN 0-87353-076-4 ACKNOWLEDGEMENT The Mathematical Association of India expresses its sincere thanks to the National Council of Teachers of Mathematics of USA for its permission to reprint its books and make these available at affordable prices to students, and libraries in India. This is a fine and generous gesture by the American mathematical community towards the Indian mathematical community and shows the common concern of professional mathematicians all over the world for excellent mathe- matics education for all. Published in India by Prof. J.N. Kapur, President, Mathematical Association of India with the permission of the National Council of Teachers of Mathematics of USA and printed by Sri Prints and Sales, Dharampura, Delhi 110006.
Contents \ INTRODUCTION 1 1. HOW TO FOLD THE BASIC CONSTRUCTIONS 4 Folding a straight line • A straight line through a given point • A line perpendicular to a given straight line • The perpendicular to a line at a point on the line • A line perpendicular to a given line and passing through a given point P not on the line • The perpendicular bisector of a given line segment • A line parallel to a given straight line • A line through a given point and parallel to a given straight line • The bisector of a given angle • The location of equally spaced points along a line • The formation of a right angle 2. GEOMETRIC CONCEPTS RELATED TO REFLECTIONS ILLUSTRATED BY PAPER FOLDING 7 Vertical angles • The midpoint of the hypotenuse of a right angle • The base angles of an isosceles triangle • The intersection of the angle bisectors of a triangle • The intersection of the perpendicu- lar bisectors of the sides of a triangle • The intersection of the medians of a triangle • The area of a parallelogram • The square on the hypotenuse is equal to the sum of the squares on the two other legs of a right triangle • The diagonals of a parallelogram • The median of a trapezoid • The diagonals of a rhombus • A line midway between the base and vertex of a triangle • The sum of the angles of a triangle • The area of a triangle • The intersection of the altitudes bf a triangle 3. CIRCLE RELATIONSHIPS SHOWN BY PAPER FOLDING 15 The diameter of a circle • The center of a circle • The center of a circle of which only a portion (that includes the center) is available

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Mathematics Through Paper Folding - MATHEMATICS T HROUGH...

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