Recent content by Gavran

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...

Your method and your result in the original post are correct because every partial differential equation that only involves derivatives with respect to one variable can be treated as an ordinary differential equation. If a partial differential equation involves derivatives with respect to more...

Dual vector spaces make analyzing and understanding vector spaces with no inner products more clear. Let us consider the set of real numbers R as a vector space over the field of rational numbers Q. The standard inner product does not exist, but we can introduce a dual space R* as a set of...

Two techniques should be applied in this case. The first one is the substitution as proposed in post #2, and the second one is the integration by partial fractions. The order in which techniques should be used first is irrelevant. If the integration by partial fractions is used first, there will...

Dealing with a dual vector space lacks bilinearity. It is more natural to use an inner product when we want to define lengths, distances, and angles; when we want to identify perpendicular vectors; and when we want to decompose vectors onto subspaces. On the other hand, an inner product lacks...