Charles Link's latest activity

Interesting to check back in with this thread and see all the new replies. On my end, I have submitted that Student Progress Report I...

I was in a similar position as you 45 years ago, and I made a successful transition to the defense industry where we did a lot of...

Full disclosure: The basic skeleton model is an included asset that comes with Blender. I did have to rig, animate it, and provide it...

You are right... my mistake... a calculation error: ## h^2 = \frac{r^2} {3} ## ## \sqrt {r^2+h^2} = \sqrt {r^2+ \frac {r^2}{3} } =...

Good one!

This figure is bounded by three circular arcs of equal radius R. The arcs are tangent where they meet. Find the enclosed area in terms of R.

Using the formula of post 22 for ## r ##, I found using ## a^2+d^2=b^2+c^2 ## that the algebra is non-trivial to show that ##...

OK, but your equation $$\sum_{i=1}^m \sin^{-1} \frac{L_i}{d}=\pi$$ is derived by assuming that the polygon is already inscribed in a...

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...

It doesn’t matter but I really should have drawn it with a,b on one side of the diameter and c,d on the other. If anyone works it feel...

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

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...

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

Since my original equation uses arcsines, and because of the differences in sine and cosine addition formulas, you get twice as many...