Recent content by Tom555

There's a theorem in Euclidean Geometry that says: "Let $\Delta$ and $\Delta'$ be two right triangles. If the hypotenuse and a leg of $\Delta$ has the same measure as the hypotenuse and a leg of $\Delta'$, then $\Delta\cong\Delta'$." Wikipedia says this is only a sufficient condition, by I don't...

Yes, thank you very much! :)

I've just started self-studying measure theory by reading Pugh's Mathematical Analysis. I'm trying to understand his argument for why the exclusion of a zero set does not change the outer measure: $m^*(E\setminus Z)=m^*(E)$: (Pugh's arugment): Let $Z$ be a zero set, $E\subseteq\mathbb{R}$, and...

Consider a commonly-used capacitor made from two circular parallel plates with a ceramic dielectric between them. The plates have 12.5 mm diameter and the whole thing is 3 mm thick with a capacitance of 10 nF. Neglecting the finite thickness and extent of the plates, what relative permittivity...