TITLE : Mathematics Through Paper Folding
AUTHORS : Alton T. Olson
PUBLISHER : Mathematical Sciences Trust Society, New Delhi
YEAR : 1975
ISBN : 0-87353-076-4
GENRE : Mathematics
PAGES : iv + 60 pages, with illustrations
FORMAT : Scanned PDF with OCR, bookmarks & covers.
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 perpendicular
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
• Equal chords and equal arcs in the same circle • A diameter
perpendicular to a chord • A radius that bisects the angle between
two radii • Arcs of a circle intercepted by parallel lines • The
angle inscribed in a semicircle • A tangent to a circle at a given
point on the circle
4. ALGEBRA BY PAPER FOLDING 18
(ax -f- by) • (cx -f dy) • Multiplication and division of a and b •
Solving x2 — px + q = 0, p and q integers
5. STAR AND POLYGON CONSTRUCTION 23
Triangle • Regular hexagon, equilateral triangle, and threepointed
star • Equilateral triangle • Isosceles triangle • Hexagon
• Regular octagon, square, and four-pointed star • Rectangle •
Square • Other relationships in the square derived by reflections
• Octagon • Regular decagon, regular pentagon, and five-pointed
star • Six-pointed star, regular hexagon, and regular dodecagon
6. POLYGONS CONSTRUCTED BY TYING PAPER KNOTS 29
Square • Pentagon • Hexagon • Heptagon • Octagon
7. SYMMETRY 31
Line symmetry • Line and point symmetry • Symmetrical design
8. CONIC SECTIONS 33
Parabola • Ellipse • Hyperbola • Similarity and enlargement
transformations
9. RECREATIONS 37
Mobius strip • Hexaflexagon • Approximating a 60° angle •
Trisecting an angle • Dragon curves • Proof of the fallacy that
every triangle is isosceles • Cube • A model of a sphere • Pop-up
dodecahedron • Patterns for polyhedrons
APPENDIX A: Plane Geometry Theorems and Related Exercises .... 45
APPENDIX B: Some Additional Theorems That Can Be Demonstrated
by Paper Folding 47
APPENDIX C: Large-Scale Figures 48
