geometry by paper folding - (13 mb pdf) - Arvind Gupta

172 Pages·2006·12.8 MB·English

MATH/STAT.

T. SUNDARA ROW S
Geometric Exercises in
Paper Folding
EditedandRevisedby
WOOSTER WOODRUFF BEMAN
PROFESSOROFMATHEMATICSIN THEUNIVERSITYOFMICHIGAK
and
DAVID EUGENE SMITH
PROFESSOROFMATHEMATICSINTEACHERS1COLLEGE
OFCOLUMBIAUNIVERSITY
WITH ILLUSTRATIONS
87
THIRD EDITION
CHICAGO LONDON
:::
THE OPEN COURT PUBLISHING COMPANY
1917
&
XC?
4255
COPYRIGHTBY
THEOPENCOURTPUBLISHINGCo,
1901
PRINTED IN THE UNITED STATES OF AMERICA
hn
HATH
EDITORS PREFACE.
OUR attention was first attracted to Sundara Rows Geomet
ricalExercises in Paper Foldingby a reference in Kleins Vor-
lesungen iiber ausgezucihlte Fragen der Elementargeometrie.
An examination of the book, obtained after manyvexatiousdelays,
convinced us of its undoubted merits and of its probable value to
American teachers and students of geometry. Accordingly we
sought permission of the author to bring out an edition in this
country, wnich permission was most generously granted.
The purpose of the book is so fully set forth in the authors
introduction that we need only to say that it is sure to prove of
interest toevery wide-awake teacher of geometry from thegraded
school to the college. The methods are so novel and the results
so easily reached that they cannot fail to awaken enthusiasm.
Ourwork as editors in this revision has been confined tosome
slight modifications of the proofs, some additions in the way of
references, and the insertion of a considerable numberof half-tone
reproductions of actual photographsinstead of the line-drawings
of the original.
W. W. BEMAN.
D. E. SMITH.
OK02

CONTENTS.
PAGE
Introduction vn
m
I. The Square i
II. The Equilateral Triangle 9
III. Squaresand Rectangles 14
IV. The Pentagon 3
V. The Hexagon , 35
VI. The Octagon 39
VII. The Nonagon 45
VIII. The Decagon and the Dodecagon 47
IX. The Pentedecagon 5
X. Series 52
XI. Polygons 67
XII. General Principles 82
XIII. The Conic Sections.
Section i. TheCircle 102
Section n. The Parabola 115
Section in. The Ellipse 121
Section iv. The Hyperbola 126
XIV. MiscellaneousCurves 131