T. Sundara Row's Geometric Exercises in Paper Folding

by Tandalam Sundara Rao

CONTENTS.
Introduction vii
I. The Square 1
II. The Equilateral Triangle 9
III. Squares and Rectangles 14
IV. The Pentagon 30
V. The Hexagon 35
VI. The Octagon 39
VII. The Nonagon 45
VIII. The Decagon and the Dodecagon 47
IX. The Pentedecagon 50
X. Series 52
XI. Polygons 67
XII. General Principles 82
XIII. The Conic Sections.
Section i. The Circle 102
Section n. The Parabola 115
Section in. The Ellipse 121
Section iv. The Hyperbola 126
XIV. Miscellaneous Curves 131



INTRODUCTION.

THE idea of this book was suggested to me by
Kindergarten Gift No. VIII. Paper-folding. The
gift consists of two hundred variously colored squares
of paper, a folder, and diagrams and instructions for
folding. The paper is colored and glazed on one side.
The paper may, however, be of self-color, alike on
both sides. In fact, any paper of moderate thickness
will answer the purpose, but colored paper shows the
creases better, and is more attractive. The kinder
garten gift is sold by any dealers in school supplies ;
but colored paper of both sorts can be had from sta
tionery dealers. Any sheet of paper can be cut into
a square as explained in the opening articles of this
book, but it is neat and convenient to have the squares
ready cut.

2. These txercises do not require mathematical
instruments, the only things necessary being a pen
knife and scraps of paper, the latter being used for
setting off equal lengths. The squares are themselves
simple substitutes for a straight edge and a T square.

3. In paper-folding several important geometric
processes can be effected much more easily than with


a pair of compasses and ruler, the only instruments
the use of which is sanctioned in Euclidean geom
etry ; for example, to divide straight lines and angles
into two or more equal parts, to draw perpendiculars
and parallels to straight lines. It is, however, not
possible in paper-folding to describe a circle, but a
number of points on a circle, as well as other curves,
may be obtained by other methods. These exercises
do not consist merely of drawing geometric figures
involving straight lines in the ordinary way, and fold
ing upon them, but they require an intelligent appli
cation of the simple processes peculiarly adapted to
paper-folding. This will be apparent at the very com
mencement of this book.

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Kindle Edition

First published August 10, 2009