Enneadecagon construction at 1.6E-11

this is the solution for compass and straight to construct a Enneadecagon with least error at 1.6E-11.

math principle of Enneadecagon construction

the pictures show the math principle of setup central angel of Enneadecagon with self accurate method.

construction a perfect Enneadecagon -2

If you have construct a 6 times angel(see last blog for the details.), it is pretty easy to use compass only to construct a perfect Enneadecagon. The right picture show the detail steps.

You can use the A19A1 angel to construct Enneadecagon also but the max error will be 3.8E-4, a slight big. But for sure , the compass will not find the error.

The nonconstructive regular polygon can be always constructed by a some complex method. But for realistic , I setup some rules for it:

1. In a 10x10 square, , the min units is 1/4.
2.the steps is not over 20 or the numbers of polygon.
3.The error is less than 0.05° for accumulation error.

My target is to finish 25 before next Chinese New year。

construction a perfect Enneadecagon-1

Enneadecagon (regular polygon with 19 sides) is also not constructable in theory. But there is some classic construction method with error 0.02 ° for the angel. Consider the accumulation error,the total erroe will be 19x0.02=0.38° which can be found by regular compass.

I had tried times and found a way to construct Enneadecagon with very little error. See right picture for details.

The idea is to construct a angel of 6 time Enneadecagon angel(360/9). Since 19 is a primer, so it is easy to use this angel to construct a perfect Enneadecagon if we can have a perfect 6 times angel.

The angel I found has error of 1E-5, the constructed Enneadecagon angel has error of 2E-5,so even for a big compass, you will be not able to find out the error as the max error is 0.00017° after construction the whole Enneadecagon。

If you not familiar for the construction with this 6time angel, see next section for details.