Recent content by nimon

Thank you for your post. Whilst I don't disagree with anything you have said, I still have a problem accepting the proposition: $$Mx+B = \pm m \sqrt{ x^{2} + y^{2} } \Rightarrow (x,y,z) \in P \cap C. $$ In fact, suppose $(x,y,z) \in P \cap C,$ then by that very proposition it follows that...

Yes I am another plucky young fool who decided to self study Spivak. I think I have found an error in his section on conic sections, but Spivak is seldom wrong and I want to be sure I'm thinking straight. Let $C$ be a cone generated by a line of gradient $m$ which goes through the origin. Then...

Cauchy's proof of the AM-GM inequality.

Hi there, I'll call the $0.1011001\ldots$ bit the decimal expansion and the $\frac{1}{2} + \frac{1}{2^{3}} + \ldots$ the series expansion. Let's define $\alpha_{k}$ to be the $k^{\text{th}}$ term in the decimal expansion of $\alpha$. After some thought I think I can show that $I_{n} = \left[...