anuttarasammyak's latest activity

I understand there is no general formula for higher order figures inscribed in a circle in terms of the radius as a function of side...

I find the above is for polygon which includes centern of circumcircle in it. As shown in #61 including polygon which does not include...

Here is an example for the case (2,3,4,5,6). In this case the sum angle is 2.578 rads which is greater than ##\frac{\pi}{2}## so the...

There are m rods length of each does not surpass sum of the others. With these rods we can make m polygons which has a circumcircle. It...

Where d is diameter of the circle re:#31. Correction: Any side must be shorter than sum of all the other sides. Heron and Brahmagupta...

In generalc case of m polygon $$\sum_{i=1}^m \sin^{-1} \frac{L_i}{d}=\pi$$ seems to hold with choice of parameter d for any...

Yes, that is Brahmagupta's formula quoted in post #33.

$$2A_{abcd}=(ab+cd)\sin\theta = (ab+cd)\sqrt{1-(\frac{a^2+b^2-c^2-d^2}{2(ab+cd)})^2}$$...

@anuttarasammyak I don't know that your method (referring to post 39) is valid. The ## x's ## are not variables with any freedom. You...

Notice when ## a+b+c-d ## is small, when the 4 sided polygon is very flat, that ## r ## is very large. The center of the circle is...

By ## d ## you are referring to the 4th side, and not the diameter of the circle. That took me a second look to figure out what you...

Thanks, I got it. I noticed that we can get unike circumcircle radius for any given a,b,c,d >0 by transforming angles of...

Confirmed. The solution that I provided in post #33 is applicable to either of the inscribed quadrilaterals that you show in your first...

Thanks for the teachings. I might have failed for null vevtors in #39. Putting d＝0 in the general solution I got familiar formula for...

continued form #31 We get three equations $$\begin{pmatrix} L_2 & L_1 & -L_4 & -L_3 \\ L_3 & -L_4 & L_1 & -L_2 \\ L_4 & -L_3 &...