Recent content by bob012345

Interesting observation! It appears so if both values are within the range of the functions. Looking at ##(a,s)## being (4,5) vs, (5,4), the area of overlap is the same over the angles but they are different situations. Here are screen shots;

I worked out the overlap of the two squares as a function of angle. Given ##a## is the half edge length of the original square and ##s## is the full edge length of the second square with one corner at the center of the first ; The area function goes as; $$ A_{\text{overlap}} = \begin{cases}...

Agreed. Now the larger square is the 1m square. The overlap depends on the relative orientation until ##s## shrinks to ##\frac{1}{2\sqrt{2}}## then it just becomes ##s^2##. Now it would be interesting to see for ##s## in that range what the overlap vs. angle function is.

The next level is if we let the length ##s## of the larger square vary, what range of values of ##s## will your statement not be true?

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two...

Well that explains my little mystery from post #18. Here is the curve for the total area of the triangle for c=d normalized to the product cd;

There are an infinite number of solutions but for each one there is a different angle and thus a different triangle. I meant for a given angle there is one solution for (a,b). Regarding the minimum, here is a graph;

The way to determine ##(a,b)## uniquely is to pick an angle ##\phi##. Then we have ##b=2tan(\phi)## and ##a=4/tan(\phi)##. As ##\phi## approaches either zero or 90 degrees, the area of the total triangle approaches infinity while the contribution of the rectangle remains constant. For the...

We wish to find the actual design to replicate it accurately.

Brand new bridge collapses in China; https://www.nbcnews.com/world/asia/nearly-2500-foot-long-bridge-collapses-china-rcna243388

Thanks. Do you have information on the power source?

Too bad they are planning on crashing it into the ocean in the not too distant future. Seems like such a waste.

Ever solve a problem so well you feel like you deserve a prize? At least that’s what I got from it.

Ok, thanks.

To me the issue is not if there is physical reality underneath what are now labeled quantum fields. It is can quantum fields be measured as distinct physical entities and what are their properties as compared to mathematical representations in some theory which are assumed to be some fundamental...