construction a Nonagon with error 4.4E-10

I got a little improvement for the Nonagon construction by compass and straight. It is a little bit complex than beofre. Details see the image.

construction a Nonagon with error 9.5E-10

I had found a method which can construction a Nonagon with hyper accuracy by compass and straight. See image for the details.

I am still working for higher accuracy for Nonagon.

construction a Heptagon with error 4E-12

A good news for me. There is a simple method that can construct a Heptagon with relative error at 4E-12,much better than last one. I am afraid that It may not have better solution for simple construction by compass and straight. But I will try further. Let's see what is next.

construction a Heptagon with error 1E-10

I go further to find more accurate method to construction a heptagon. The new method has relative error at 1.14E-10,which is much better than before.The method is not complex so a heptagon can be constructed in a few steps with extremely accuracy.

another simple and accurat classic method to construction the Heptagon

I am happy to find another simple method with relative error 5.7E-9. it is only 6 steps. See the image for the details.

construct heptagon with error at 2.3E-9

It is my pleasure to find a method go beyond 1E-8 for construct Heptagon with classic method. I doubt first if it is possible to use simple method to construct heptagon with relative error less than 1E-8. It seems there is possibility for relative error less than 1E-9. let me try further.

the detail construct steps are on the image.

improved the method to construct Heptagon with error 4E-8

I checked last method and found it can be simplified. The details are on the image.

another simple way to construct Heptagon with hyper accuracy

I found another simple construction method for Heptagon with relative error 4.4E-8.,a tiny better solution than last one. Hope some one will enjoy it.

Hendecagon construction with hperaccuracy

I found a method which can construct hen-decagon(11sdies) with relative error less than 3E-8. The picture show the principle and detail construction steps.

the study of a curve to 3 points with same sum of distances:case 1

We all know that a curve to two points with same sum of distances is ellipse.

But how about to 3 points?

I try to study this case as I haven't find out any mention about it.

My study show that the curve is interesting, I start from ths most simple case:

3points in one line and with equal distance c , the sum of the distance is p and one important figure is, p=3c,

another important figure is p=2c which is limitation of the p. if p=2c, that means the curve is a point.

figure1 is p<3c,>> 2c,
figure 2 is p=2c,which like an eye
figure 3 is p>3c, similar as fig1
figure 4 is p very close to 2c, which like a ellipse

the blue curve is real curve and brown curve is ellipse which simply for reference.

construct a Nonagon with Hyper accuracy by compass and straight

I just found another new method which can create Nonagon central angel with hyper accuracy. The relative error is about 4.6E-8. I think it is the best accuracy so far.

a new method to construct heptagon with hyper accuracy

When I checked wiki for heptagon construction method, I found there is a method with 10E-7, a very very accuracy and simple method. I try again to find a better accuracy method and did it. the picture show the math principle and detail construction step. the accuracy is 5E-8,about 10 times better.I am sure it is the best one so far.