(512) I am not a trisector.

  Underwood Dudley in Department of Mathematics Depauw University, explained about trisector in his writing, 'What To Do When the Trisector Comes'.

  A trisector is a person who has, he thinks, succeeded in dividing any angle into three equal parts using straightedge and compass alone. He comes when he sends you his trisection in the mail and asks your opinion, or (worth) calls you to discuss his work, or (worse still) shows up in person.

  One obvious characteristic of trisectors is that they are old. The typical trisector heard of the trisection in his geometry class, but did not succeed with his construction until many years later, usually after retirement. "His" in the last sentence is not sexist because almost all trisectors are male. From the two female calculation that we can be 95% sure that proportion of female trisectors is less than .04. Women have too much sense to waste time on such things. Trisectors are old men. An Illinoi lawyer wrote in 1953.

  Underwood said those trisectors are mathematical cranks (persons with a strange idea, because trisection with compass and straightedge is mathematically proved impossible.

  I came across this article while I'm searching for the ways of how to divide some angles into three equal parts. I am old and retired man but the big difference is that I don't mind what kinds of tools are used to trisect the angles. So, I am not the trisector at all. I just want to make a handmade protractor. My goal is to get an angle of one degree. I just wondered how each angle line is drawn on a protractor when I was a child. I had many questions around me when I was small but forgot most of them. But now I'm old and have much time to remember and think of some of them. So, I decided to try challenging those questions. And handmade protractor is one of them.

Here is a plastic protractor and my hand made one is next.

My plan was as follows,

(1) Draw an angle of 72 degrees.

     I should learn how to draw a regular pentagon.

(2) Get a 24-degree angle by dividing 72 into three equal parts.

     72÷3=24

(3) Get an 8-degree angle by dividing 24 by three.

     24÷3=8

(4) Get a 4-degree angle by dividing 8 by 2.

     8÷2=4

(5) Get a 2-degree angle by dividing 4 by 2.

     4÷2=2

(6) Finally get a one-degree angle by dividing 2 by 2

     2÷2=1

  First, I must learn how to draw a regular pentagon.

I can draw a right pentagon by knowing the ratio of red segment and blue one is (√5+1) : 2.

Next, I picked up one tool to get a trisection. It is a L-shaped ruler. Following drawings show how to divide an angle into three equal parts.

I used this triangle instead of the L-shaped ruler. I use two line and two dots in red on the ruler.

 

This is how a 72-degree angle is divided into three equal parts.

72°÷3=24°

I am dividing a 24-degree angle into three equal parts of 8 degree angle.

I know how to divide any angle into two equal parts.

Finally, I got a one-degree angle.

Now I'm satisfied to finish my challenge that I thought of but gave up in my school days.

Thank you for reading.

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