All Questions

5k views

Taking Seats on a Plane

This is a neat little problem that I was discussing today with my lab group out at lunch. Not particularly difficult but interesting implications nonetheless Imagine there are a 100 people in line to ...
700 views

Conjugate subgroup strictly contained in the initial subgroup?

Probably a very stupid question: Let $G$ be a group, $H\subset G$ a subgroup, $a\in G$ an element. Is it possible that $aHa^{-1} \subset H$, but $aHa^{-1} \neq H$? If $H$ has finite index or finite ...
3k views

Fibonacci modular results

Can any one give a generalization of the following properties in a single proof? I have checked the results, which I have given below by trial and error method. I am looking for a general proof, which ...
779 views

3k views

Prove $\sin(A+B)\sin(A-B)=\sin^2A-\sin^2B$

How would I verify the following double angle identity. $$\sin(A+B)\sin(A-B)=\sin^2A-\sin^2B$$ So far I have done this. $$(\sin A\cos B+\cos A\sin B)(\sin A\cos B-\cos A\sin B)$$But I am not sure ...
61 views

2k views

Motivation behind standard deviation?

Let's take the numbers 0-10. Their mean is 5, and the individual deviations from 5 are -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 And so the average (magnitude of) ...
4k views

Normal subgroup of prime index

Generalizing the case $p=2$ we would like to know if the statement below is true. Let $p$ the smallest prime dividing the order of $G$. If $H$ is a subgroup of $G$ with index $p$ then $H$ is normal. ...

15 30 50 per page