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Let ## (x_1,y_1) ## be a point on the curve ## f(x)=4-x^2 ##, which is the closest point on the curve ## f(x) ## to the curve ##...

The other day a friend of mine gave me the above problem which I found rather interesting. I was able to get a numerical solution...

There are Figures 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, and 19 in the same text...

Ok, there must be some rule I’m missing, after which the penny will drop. Forgive my stupidity. How is the X1 (or U) junction defined...

It depends on how X1, X2, and X3 are interconnected with W4, W5, and W6. See again Figure 4-D7 (the third image on the right).

Yes, you are right. That means X1 lags H1 by 30° in group 1, and X1 lags H1 by 330° in group 11. Both examples are correct. See Figure...

Thanks, so by that definition the group 1 will be a 30°, and the group 11 a 330°? There were two other examples: I make these group 7...

This is group 1. If H1 points at 12 o'clock, X1 will point at 1 o'clock. This is group 11. If H1 points at 12 o'clock, X1 will point at...

The substitution ## y_1=10^y ## simplifies the equation $$ 10^ydy=\frac{dx}{x\ln10} $$ to the equation ## dy_1=dx/x ##. The general case...

In the general case, the time that the ant needs to reach the end of the rope is $$ T=\frac cv(e^\frac v\alpha-1) $$, where ## c ## is...

You can notice from the animation that the ant absolutely moves at an increasing speed, while the rope end absolutely moves at a...

It is good to see how problem-solving by humans can be enriched by artificial intelligence. It can also be seen that problem-solving by...

https://en.wikipedia.org/wiki/Anthony_Leggett https://www.nytimes.com/2026/03/11/science/anthony-james-leggett-dead.html...

Happy Groundhog Day 2-2-26. The above is a photo of the snowman that I have in my backyard. It now measures about one inch over 4'0"...

I remember the thread posted by @chwala in 2024, which is used as a reference in the article. The geometric solution provided by...