pasmith's latest activity

I would rotate the sphere so that one point is at the north pole (0,0,1). Then ##\theta## is just the colatitude of the image of the...

If ##A## is invertible, then solving ##Ax = b## by Gaussian elimination where ##b## consists of zeros except for a 1 in the ##i##th row...

We don't solve linear systems numerically by finding an inverse matrix; that is incredibly inefficient. Instead we use other methods...

Your working appears to be correct, and I obtained the same result by considering the discriminant of ##f##. What did you do to verify...

Coordinates are independent, whether orthogonal or nonorthogonal. Introducing such a dependency restricts you to a curve or a surface...

Alternatively, we can also consider that the general solution of ##F_{n+2} = F_{n+1} + F_n## is $$\begin{split} F_n &= A \left( \frac{1...

A slight correction is indeed required. From ##a_n \geq 1## we have ##a_n \varphi \geq \varphi ## so that $$ |a_{n+1} - \varphi| \leq...

There is a much easier way to arrive at these results. From ##a_{n+1} = 1 + a_n^{-1}## and the definition of ##\varphi## we can obtain...

So that we understand the proofs, and can satisfy ourselves that they are indeed correct proofs. We don't take other people's word for...

It is a fact of basic group theory that conjugation preserves the order of an element (because conjugation is an isomorphism from a...

A generalization is to fix ##g: [0,1] \to \mathbb{R}## and let $$f_n : [0,1] \to \mathbb{R} : x \mapsto \begin{cases} ng(nx) & x < \frac...

I was going to append this to @chwala's thread here, but thought it deserved a new thread. For ##n \geq 1##, define $$f_n : [0,1] \to...

Consider also ##e^{-n\sin \theta}## for ##\theta \in [0, \pi]##.

Responses, like the original post, should be typed and make use of LaTeX rather than screenshots.

I was working at the UK's Ministry of Defence just over 10 years ago when they rolled out Office 365. This involved the MOD making...