# 3 Useful Layouts - For Fun and Function

# Table of Contents

Disclaimer and Warning

How to Read this Book

Chapter 1

How to Lay Out a Large Right Angle

#### I. The Amazing Right Angle

#### II. Methods for Laying Out a Right Angle

II.A. Square Implements

II.B. The Pythagorean Theorem

#### III. Two Practical Examples of Right Angle Layouts

III.A. Gather Our Tools

III.B. Clear Out a Work Space

III.C. Choose a Corner Point and Mark It

III.D. Establish 6’ Line

III.E. Strike 8’ Arc from the Anchor Corner

III.F. Strike 10’ Arc from End of 6’ Line

III.G. Establish 3rd Point

III.H. Complete the Right Angle Line

#### IV. Recheck & Reiteration

IV.A. Remeasure All Points to Be Sure

IV.B. Don’t Forget Pythagoras

IV.C. Customize the Ratios

IV.D. Go Forth and Be Square

Chapter 2

How to Find the Radius of an Arc

#### I. To Lay Out an Arc with Limited Information

I.A. Height and Width Are Known

I.B. Radius Determined by Math

#### II. The Derivation of the Arc/Radius Formula

II.A. The Properties of an Arc

II.B. A Chord and a Segment of a Circle

II.C. Chord with Known Radius Leads Us to an Unknown Radius

II.D. Pythagorean Theorem Solves for “R”

#### III. Use the New Formula to Find the Radius

III.A. If “h” and “L” Are Known, Do the Math

III.B. Determine the Parameters of a Curve in the Garden Path

#### IV. Radius Set, Scribe Arced Curve in the Garden Path

IV.A. Start at the First Rock

IV.B. Adjust at the Peak Rock and Continue the Arc

IV.C. Stop at the Last Rock

IV.D. Behold a Perfect Arced Curve

Chapter 3

How to Make an Ellipse Machine

#### I. What is an Ellipse?

I.A. Two Fixed Points

I.B. Sum of Distances From Any Point on Ellipse Always Equal

#### II. The String Method

II.A. Materials and Tools

II.B. Axes and Intersections

II.C. Pushpins and String

II.D. String and Pencil Draw an Ellipse

#### III. The Trammel Method

III.A. Trammel Beam

III.B. Trammel Points

III.C. Elliptical Symmetry

III.D. The Trammel Ellipse

#### IV. The Ellipse Machine

IV.A. Grooves Instead of Lines

IV.B. Large Scale Scenic Method

IV.C. Create the Channels with Panels

IV.D. Lay Down the Paper

IV.E. Set Up the Trammel Bar

IV.F. Draw Ellipses

IV.G. Use Drawings to Create Templates

IV.H. The Power of the Ellipse Machine

Appendix 1

How to Double Snap a Long Chalk Line

1. How a Snap Line Works

2. How to Double Snap a Chalk Line

3. Double Snap Good to About 30’

Appendix 2

Simplification of Arc/Radius Formula

Appendix 3

Step-by-Step Calculations to Find the Radius of an Arc

Appendix 4

The Layout of a Semicircle

1. Length of Chord is the Diameter

2. Half the Diameter is the Radius

3. Process Illustrated Step by Step

Appendix 5

Locating the Radius Point of an Arc

1. Radii Struck From Along an Arc Intersect at the Radius Point

2. So Do Radii Struck From the End Points of an Arc

3. Two Arcs Struck From the End Point Locate the Center

4. Brief Summary

Appendix 6

Examples of Distances from Random Points

Appendix 7

Acquiring Material for Spacer Strips and How to Cut Them

1. Acquire 1/16” Spacer Material

2. Slice Against Durable Straightedge

3. Lay Out 1” Increments

4. Align Straightedge & Carefully Cut Strips

5. Cut One Strip in Half

Appendix 8

How to Make a Template of our 14” by 18” Ellipse

1. Acquire 11” x 17” Paper

2. Do One Side at a Time

3. To Complete Template, Tape Together the Two Sides

Index