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I teach math at St. John Fisher College in Rochester.


1d
comment Geometry - Volume of a distorted tent
If we redefine $h(x)$ as the altitude of the triangle formed by the segment through $x$ parallel to the $a$ side of the base, where $0 \le x \le b$ is taken as above to denote distances measured along the center line of the rectangle parallel to side $b,$ then it seems we get the same formula for $h(x)$ as used above. The triangles formed are still parallel to each other and the volume added is $(1/2)a*h(x) dx,$ so it seems the same formula as above should be right for the skew case also.
1d
awarded  Constituent
2d
answered Geometry - Volume of a distorted tent
2d
comment Geometry - Volume of a distorted tent
Can we assume the base of the tent is a rectangle, and the sides go up into a creased "top" (imagine there is a pole holding the canvas up)? And you want to consider the case where the holding pole is not parallel to the plane of the base?
2d
comment Congruence properties of $a^5+b^5+c^5+d^5+e^5=0$?
Did Duncan Moore notice the divisibility by at least $2^5$ in a paper or elsewhere, and then state he could not establish it? If so maybe this question is a bit advanced for this site, and would be better on a research site like Overflow.
2d
comment How to prove this statement about this relation:
Take e.g. $x=5$. If $5 \sim 5^2$ that would imply, since $5^2|5^2$, that also $5^2|5.$ So it seems the only case of $x \sim x^2$ would be $x=1.$
2d
revised Polynomials with specified ranges in intervals
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2d
revised Polynomials with specified ranges in intervals
added 304 characters in body
2d
comment Function's analytic continuation is its own derivative
If as this comment starts you only want the continuation to match the derivative at the endpoint $z$ then consider $f(z)=z^2$ in a neighborhood of zero. Then the continuation of $f$ is itself, and its derivative at zero is $0$, matching $f'(0)=0.$ But in the rest of the comment you seem to say the opposite, that at each point of the path the continuation matches the derivative... So I don't (yet) see which you mean, that is, your last comment seems to start with one version and continue with the stronger condition along the whole path.
2d
comment Function's analytic continuation is its own derivative
If the path is say $\gamma(t),$ does the requirement mean that at each $t$ we have $h(t)=f'(t),$ where $h$ is continuation of $f$ along $\gamma(t)$, or does this only need to hold at the endpoint of $\gamma$ (i.e. on the return to $z$)?
2d
revised Polynomials with specified ranges in intervals
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2d
answered Polynomials with specified ranges in intervals
Dec
18
revised No sum of three numbers equals another number in set
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Dec
18
comment Number of Dyck paths from $(0,0)$ to $(2n,k_1)$ if allowed to go below the $x$ axis
Is it allowed to go below the line $y=k_2$? If not it looks like one could add $-k_2$ to each path to get it as usual not going over $x$ axis, but this would change (raise) the start and finish points also, making it related but not identical to Dyck path counts. May be one can adjust those results...
Dec
18
comment No sum of three numbers equals another number in set
@BrianM.Scott I have tried for a fix to your commented objection, and would appreciate it if you'd have a look to see if something else needs to be done. Thanks in advance if you do.
Dec
18
revised No sum of three numbers equals another number in set
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Dec
18
revised No sum of three numbers equals another number in set
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Dec
17
comment No sum of three numbers equals another number in set
@BrianM.Scott Good point, I'll roll back for now until/unless I get a fix for that case.
Dec
17
answered No sum of three numbers equals another number in set
Dec
17
comment How prove for any $k$ then have $a^2_{1}+a^2_{2}+a^2_{3}+\cdots+a^2_{k}=m^3$
@TitoPiezasIII I looked at that identity, and it seems interesting. (Gave the answer an upvote)