33,376 reputation
894227
bio website blog.plover.com
location Philadelphia, USA
age
visits member for 2 years, 8 months
seen 15 mins ago

I am Mark Dominus, an amateur.

I have a blog that often carries articles about mathematics.


1h
comment $27 | (2x+1)^2 \implies 2x$ is a multiple of 9?
@belgi Because I don't feel like I understand what is really going on here. If OP had provided a source, I would post an answer that says definitively “there is a misprint” or “you misunderstood”. But as it is I don't feel that I have the true answer. You should feel free to repost my comment as an answer if you like. (Added: having seen that N.S. and graydad have posted much more pertinent replies, I am glad I did not post my observation as an answer.)
1h
comment $27 | (2x+1)^2 \implies 2x$ is a multiple of 9?
That is certainly wrong, because $x=4$ gives $28\mid (2x+1)^2$, but $2x$ is not a multiple of 9. There is an error somewhere.
2h
comment How do you show Euler characteristic of any convex polyhedron is $2$?
Closely related question by the same user: Euler characteristic of a convex polyhedron
4h
comment Are exponents with a base very close to $1$ (such as $1.0001$) useful in Mathematics?
in this answer I quoted an explanation of why tables of logarithms were first calculated to base $1+\epsilon$ (actually the very first tables were calculated to base $1-\epsilon$).
5h
comment Is this correct way to prove that { $uv$ $\mid$ $u$ and $v$ are strings over $(0,1)$ & $|u| = |v|$ } language is not regular?
Would you like an answer to your question, explaining where the error is in your application of the pumping lemma? Or do you feel that your question has already been answered?
5h
comment Continued fraction of the golden ratio
possible duplicate of Where did the negative answer come from in $1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{\ddots }}}$?
5h
comment incorrect notation in math?
Sorry, I don't follow your reasoning. There is no $\sqrt[3]2$ in my post.
23h
comment Third degree polynomial with unknown coefficients $q^3-3aq^2+b^2q+c = 0$
Use Vieta's formulas.
1d
comment Parametrising the unit circle without sine and cosine
@mvg Oh, of course the derivatives don't match up. Do you think I should delete the suggestion, or do you think the mistake is instructive enough that I should leave it?
1d
comment Parametrising the unit circle without sine and cosine
Don't the derivatives match up at $t=\frac12$? If not, please pardon my error. I did not actually do the calculation, which is why I posted only a comment, rather than an answer.
1d
comment How can I prove that a graph with a required amount of edges per node is invalid?
Yes, each edge contributes 1 to the total degree of each of its two endpoints.
1d
comment Mathematical results that were generally accepted but later proven wrong?
'Obvious' theorems that are actually false might also be some use.
1d
comment Mathematical results that were generally accepted but later proven wrong?
Is this different from In the history of mathematics, has there ever been a mistake?
1d
comment How can I prove that a graph with a required amount of edges per node is invalid?
A graph can have an odd number of edges, but the sum of the degrees of the vertices must be twice the number of edges, and so must be even.
1d
comment How can I prove that a graph with a required amount of edges per node is invalid?
I was mistaken, it's 13.
1d
comment How can I prove that a graph with a required amount of edges per node is invalid?
Do you know the theorem that the sum of the degrees of the vertices must be even? But in your example it is 11.
1d
comment Parametrising the unit circle without sine and cosine
Offhand it seems to me you could take $\gamma : t \mapsto \left\langle 1-4t, \sqrt{1-(1-4t)^2}\right\rangle$ for $t\in\left[0, \frac12\right)$, then $t\mapsto \left\langle 4t-3, -\sqrt{1-(4t-3)^2}\right\rangle$ for $t\in\left[\frac12, 1\right)$. This is piecewise, but still smooth.
1d
comment How can I prove that the square root of two prime numbers multiplied is non-rational number?
You should be able to adapt the proof that $\sqrt 2$ is irrational. Do you know that proof? That seems to be a logical place to start.
1d
comment Do there exist integers s and t such that 11s + 9t = 1?
I don't know why this got a downvote; I think it's a great answer.
1d
comment Showing $p^2 + q^2\ne r^2$ for primes $p, q, r$.
Too much hint. ${}{}$