Special_Tools for Angle Trisection

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Trisecting an Angle
Special Tools

### Trisection using Special Tools

#### Drafter's Triangles

Drafter's Triangles is shown in the figure shown below.

Two trangles CDE & LMN are the commonly used ones in drafting.

Draw a unit circle with center "O".

Define an angle to be trisected AOB, with point "A" on this unit circle.

Angle AOP is 90 degrees and length OP = cos(AOB)=a .

Point "Q" is (2a, 0)

Define a point "R" on y-axis such that OR = 3 times radius of unit circle.

Define a point "S" such that RS = OQ = 2a

********** drafter's_triangles_desc.dwg** ********

Trisection procedure.

"C" stays on X-axis,and CD passes through the point "T"

The bases of the triangles CE and MN are on the same line.

The line LM passes through point "S"

Then when the corner point M comes on the y-axis, the trisection is done.

You can see the process in **animation**

#### Example Picture 1

This is a picture of the actual operation. The radius of the circle is 2 inches, and the angle to be trisected is 60 degrees.

The author used a digital camera ,which stores image in JPG file(the file size is around 800 KB).
The steps taken are:

1. Take a photo of the final position of triangles.

2. Transfer the file to my PC.

3. Open the file using **"Insert"-> "Raster Image"** option in AutoCAD.

4. Create points on the photo, and measure the resulting angle using **"Dimension" -> "Angular"** option.

5. In Command line window, type **JPGOUT** to save the result in JPG file.

********** triangles_example_60_deg.dwg** ********

#### Example Picture 2

A 30-60 deg drafting triangle can be replaced by any right angled ruler.The author used
a typical Japanese Carpenter's Square (Its width is about 1/2 inch).

********** triangles_example_60_deg_2.dwg** ********

**To create this drawing and animation: **

** Load triangle.lsp (load "triangle")**

Then from command line, type **triangle **

For a quick look , type **test_triangle **

Animation file creation: **animation_triangle**

#### Example Run: 60 degrees case:

********** triangles_trisection_60_deg.dwg** ********

1. Yates, Robert Carl : "The Trisection problem",pp. 43 - 44.

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All questions/suggestions should be sent to Takaya Iwamoto

Last Updated Nov 22, 2006

Copyright 2006 Takaya Iwamoto All rights reserved.
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