Ruler & Compass: Practical Geometric Constructions

by Andrew Sutton

Overview

How do you draw a heptagon? What about a heptakaidecagon? How do you fit circles perfectly into triangles? And around them? If the computer is down - could you do it with ruler and compass? In this unique pocket book, Andrew Sutton guides you through the once treasured principles of ruler and compass constructions, used for centuries by architects, carpenters, stonemasons and master craftsmen.
Designed to last until the lights go out, this is a timeless book. WOODEN BOOKS USA. Small books, BIG ideas. Tiny but packed with information. “Stunning" NEW YORK TIMES. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST.

Product Details

ISBN-13:	9781952178092
Publisher:	Wooden Books
Publication date:	03/15/2022
Series:	Wooden Books North America Editions
Pages:	64
Product dimensions:	5.50(w) x 6.75(h) x 0.33(d)

About the Author

Andrew Sutton is a high school mathematics teacher based in the UK. He has taught in London and New York and has a special interest in mathematics in art.

Read an Excerpt

The art of geometric construction can be traced back to the widespread, possibly universal, practice of marking out simple forms and measures on the Earth using pegs and cords – geometry, literally Earth measure. Examples include ancient Egyptian rope stretchers, or harpenodaptai, who re-established land boundaries after the annual Nile flood, and ancient Indian altar construction techniques found in the Vedic Sulbasutras, the oldest surviving texts with geometric instruction. In time this became the more familiar mathematical discipline, practiced at a smaller scale. Plato (d. ca. 347 bc) first stipulated the strict use of only ruler and compass, the ideal simple forms of straight line and circle.
This book is intended as a small practical guide to the field, inspired by the artisans' manuals penned by Abu'l-Wafa' al-Buzjani (d. 998) and Albrecht Dürer (d. 1528). Some mathematical context and history is given, but no proofs. Unless noted, all constructions are mathematically exact. Readers are highly encouraged to try their hand at some of them – there is no substitute for actually taking ruler and compass to paper.
This book uses a simple code. Line ab means draw the straight line that passes through a and b. Segment is used in place of line for the section of a straight line defined by two endpoints. Circle o-a means draw a circle centred at o and passing through a. Circle radius ab centre o means draw a circle of compass opening length ab centred at o. Arc is used in place of circle for drawing only part of the circle. Sometimes, extra points are given to help improve accuracy when drawing, for example, line acb, or circle o-ab. Newly found points are noted in brackets. Occasionally a line made possible by new points is assumed drawn, and merely noted, and stages may also be grouped together for brevity. Fear not. All will be clear.

Table of Contents

Introduction 1

Fundamentals 2

Perpendiculars 4

Parallels 6

Triangles 8

Squares & Rhombuses 10

Square Areas 12

Hexagons & Dodecagons 14

Octagons 16

Triangle Centers 18

Inscribed Circles 20

Tangents 22

More Tangents 24

More Inscribed Circles 26

Dividing a Segment 28

Means 30

The Golden Section 32

Pentagons & Decagons 34

Possibilities 36

Neusis 38

Heptagons 40

Approximate Polygons 42

Dividing Rectangles 44

Proportional Rectangles 46

Spirals 48

Ellipses & Ovals 50

Rusty Compass 52

Compass Alone 54

Appendix - Grid Constructions 56

Appendix - Polygon Combinations 58