construct a peferect Hendecagon

Hendecagon is nonconstructive polygon by compass also. In wiki, there is a method with the central angel error is 0.01°. So accumulated error is about 0.1°.

I had found a very precis method which the central angel error is 0.000026°。 The accumulation error is 0. 00026°，which is nearly perfect for the compass and straight.

And the more interesting is ,when you finish the construction ,the line and arc like paint. see the right picture.

I will not post the details and you can try yourself by stating from the two little squares in the central.

Good Luck and have a fun.

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.

Improve the classic method to construction a Heptagon

I modify the construction method which is more brief.

Draw a perfect Heptagon with classic method

Heptagon is not constructable by rule and compass theoretically. But there is some classic method to construct Heptagon with small error about one tenth degree.(Dixon)

I find a way which much much better close to perfect Heptagon with error -0.0018 degree. details see the picture at right.

I write down the detail step in the picture.

I found out this method by study the 12 orthogons recently. Actually, I found a another way with pentagon first which I will post later.