Recent content by Gavran

I remember the thread posted by @chwala in 2024, which is used as a reference in the article. The geometric solution provided by artificial intelligence is also described in the article. In this case, we cannot use it for comparing human labor with artificial intelligence labor because nobody...

A veridical paradox is one of three types of paradoxes, which is what defines it as a paradox.

100 kg of potatoes consists of 99% water. After some water evaporates, the potatoes consist of 98% water. What is the new weight of the potatoes? The answer is 50 kg. The explanation is simple. 100 kg of potatoes consists of 99% water and 1% dry matter, so the weight of the dry matter is 1 kg...

This can also be shown in the following way. ## \begin{align} &\arctan\frac\alpha c+\arctan\alpha=\arctan c\nonumber\\ &-\arctan\frac{\alpha}{\alpha\beta}+\arctan\alpha=\arctan c\nonumber\\ &-\arctan\frac1\beta+\arctan\alpha=\arctan c\nonumber\\ &\arctan\alpha-(\frac\pi2-\arctan\beta)=\arctan...

The equation ## C=A+B ## is actually Euler's formula $$ \arctan\frac12+\arctan\frac13=\frac\pi4 $$, and there are three more formulas of this kind. Hermann's formula $$ 2\arctan\frac12-\arctan\frac17=\frac\pi4 $$ , Hutton's or Vega's formula $$ 2\arctan\frac13+\arctan\frac17=\frac\pi4 $$ , and...

There are four formulas of this kind. Euler's formula $$ \arctan\frac12+\arctan\frac13=\frac\pi4 $$ Hermann's formula $$ 2\arctan\frac12-\arctan\frac17=\frac\pi4 $$ Hutton's or Vega's formula $$ 2\arctan\frac13+\arctan\frac17=\frac\pi4 $$ Machin's formula $$...

Based on the previous posts, it can also be shown that A+B+C=D for the angles A, B, C, and D in the next picture. Or A+B+C+D=E for the angles A, B, C, D, and E in the next picture.

I think you are right, and the correct answer is d. A copper shield can be better than a steel shield against a high-frequency magnetic field, but based on the picture from the original post, there is only a static magnetic field.

## P(X=g) ## - probability that we have g green cards remaining ## P(X=b) ## - probability that we have b blue cards remaining ## P(X=r) ## - probability that we have r red cards remaining ## E ## - expected number of cards remaining $$...

The author (A Student's Guide to Vectors and Tensors, by Daniel Fleisch, Cambridge, 2012., Chapters 4.5 and 4.6) does not mention a dual vector space. He does not speak in the context of a vector space and its dual vector space. He speaks in the context of the same vector space with two...

Agree with the above. “Find x where x2=4” versus “Find x where x2=4 and x>0"; two different problems with two different sets of solutions. Or post #28 versus post #31 ; also, two different problems with two different sets of solutions.

One more solution with three congruent equilateral triangles.

https://en.wikipedia.org/wiki/Linear_differential_equation#Homogeneous_equation_with_constant_coefficients...