Servaes

Graduate student mostly dabbling in algebraic geometry.

 Apr 21 comment Constructing the asymptotes of a hyperbola by compass and straightedge.The last step of the algorithm is explicitly specified to work only for rectangular hyperbolas; this step does not work if the hyperbola is not rectangular. Apr 19 comment Constructing the asymptotes of a hyperbola by compass and straightedge.Thank you for the good reference. I'm not assuming my hyperbola to be rectangular, but it seems the construction can be made to work in the general case as well. I'll look into this later today. Apr 19 comment Constructing the asymptotes of a hyperbola by compass and straightedge.Good question; one is given only the hyperbola, and one can choose arbitrary points on it. So your example is perfectly allowed. Apr 19 comment Is $N_{A_7}(H) = H$, with the following $H$?So this reduces to a question about $A_6$, in which $H$ has index $15=3\times5$. But $A_6$ has no subgroups of index $3$ or $5$, and $A_6$ is simple. Apr 19 comment Is $N_{A_7}(H) = H$, with the following $H$?It is not transitive as $1$ is fixed by $H$. Apr 19 asked Constructing the asymptotes of a hyperbola by compass and straightedge. Apr 7 revised How many ways are there to assign $20$ different people to $3$ different rooms with at least $1$ person in each room?added 2 characters in body Mar 30 comment How many ways are there to assign $20$ different people to $3$ different rooms with at least $1$ person in each room?I simply wrote $3^{20}=3\times 3^{19}$, if that's what you mean? Mar 30 comment Proving a clique number and independence number?@dewick49 Thank you for the correction, I misread. If the picture is all you have, then necessarily all your findings are found visually. Mar 30 revised Proving a clique number and independence number?added 602 characters in body Mar 30 comment Proving a clique number and independence number?Yes. If you have a description or characterisation of the graph other than this picture, it would be useful to include it. Mar 30 answered Proving a clique number and independence number? Mar 30 comment Determining if two transformations are similar using concept from Jordan Form.Yes. What are your thoughts on the problem so far? Where did you get stuck? Mar 30 answered What is the dimension of the orthogonal complement of a hyperplane? Mar 30 answered How many ways are there to assign $20$ different people to $3$ different rooms with at least $1$ person in each room? Mar 30 revised Let $L$ be a subgroup of $\mathbb{Z}^3$ of index $16$. What are the possibilities for $\mathbb{Z}^3 /L$?added 53 characters in body Mar 30 comment Discrete Math Induction Proof Help With QuestionYou then proceed correctly, but make a misstep at the second to last step: $$6\frac{n^2+n}{2}-\frac{6n}{2}=\frac{6n^2+6n}{2}-\frac{6n}{2}=\frac{6n^2+6n-6n}{2‌​}=\frac{6n^2}{2}=3n^2.$$ ... I seem to be having some problems with LaTex myself. I hope the point is clear. Mar 30 comment Discrete Math Induction Proof Help With QuestionHow do you justify the first step? It makes no sense, you are no longer summing over anything... And where did $n$ go? Mar 30 revised Discrete Math Induction Proof Help With Questionadded 1 character in body Mar 30 revised Let $L$ be a subgroup of $\mathbb{Z}^3$ of index $16$. What are the possibilities for $\mathbb{Z}^3 /L$?added 772 characters in body