joelthelion

This is both true and a bit dumb. We are all responsible for these emissions by buying and burning these fuels (most of the time indirectly).

I wouldn't be surprised if Trump threatened military action in return, should Canada go forward with it. I mean, it sounds crazy to write it, but is it really too crazy for Trump?

I've implemented a gradient descent algorithm in python to optimize the shape, and I get essentially the same thing:

I'm changing the title to solved :)

Here's the code: https://pastebin.com/wKvhVvQg

Reading the paper, exercise alone had no effect on these "biological clocks". So, the results are promising, but given the lackluster results of the trial on other outcomes (blood pressure, mortality, falls, etc.), I'd be cautious before jumping to conclusions.

I think the main question is how exercise alone compares to exercise +supplements. If I have time later I'll try to dig into the paper.

Here's another solution, that is suboptimal but might be preferable to the soap bubble solution in practice: an ellipse with long axis 1.592 and short axis 0.972. This should be close to the optimal ellipse (I used Kepler's approximate P=pi * (a+b) formula for the perimeter). It gives an area of 4.861 which is close enough to the current optimum, and looks like this:

You have the best solution so far, but I wouldn't call it solved yet, since we don't have any proof or indication that it is the best solution that exists.

In my case, yes, because I don't have much to attach the mesh wire to.

Hi, I'm familiar with the concept of Euler-Lagrange equations, however I wouldn't know how to use them in practice to solve a problem like this one. ChatGPT isn't very helpful and suggest a single circle cut in half is the optimal solution, even when I tell it to use Euler-Lagrange.

It looks good, however when I compute the area, I get 4.4872..., which is less than what I get for the single circle. I could be wrong though, as others seem to be getting 4.94.

Edit: I found my mistake! I was using the wrong formula for the altitude of the equilateral triangle. Now I get 4.9458..., which is by far the best result so far. Thank you!

The best I was personally able to obtain is the circle divided by a wall.

I initially asked this question on the mathematics stack exchange: https://math.stackexchange.com/questions/5035579/area-maximization. Of course, it got closed for no reason, but before it did, someone offered the following solution: join two circular arc (subtended at angle 240∘ with respect to their center) at their end points, add a line segment between the end points, you can achieve an area ∼4.9457788. Recomputing the area of their solution, I get ~4.49 instead, but I'm not sure I got it right...

dupe