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Jul
5
comment Determine largest area of house using geometry
Cut the rectangle of dimensions $2a\times(15-a)$ into two rectangles of dimensions $a\times(15-a)$ and your assumption is justified geometrically. :)
Jul
5
comment Motion on a parametric surface
Yes, a geodesic is definitely what you're looking for. In general, you have to solve an ODE involving the differential geometry of the surface to find it, and I doubt you can get a closed form except in very special cases. Unfortunately, this is where the extent of my knowledge ends, so I'll let someone with more expertise provide a full answer.
Jul
5
comment Motion on a parametric surface
The question isn't entirely clear. Are you looking for a geodesic path along the surface with specified initial point and tangent vector?
Jul
4
comment Integers on a blackboard
@Michael: I'd say if there is no probability distribution specified in the question, then it's probably(?) not a probability question. Otherwise any problem involving arbitrary choices becomes a probability problem.
Jul
4
comment Drying blood - an algorithm for calculating the geometry of blood stains
I feel like this is a little too vague to be a mathematical question.
Jul
4
comment Next generation numbers
This looks like a duplicate of either Is there is a number system which is extension of complex number system? or The largest number system, or both.
Jul
4
reviewed Approve Show that $\displaystyle{\frac{1}{9}(10^n+3 \cdot 4^n + 5)}$ is an integer for all $n \geq 1$
Jul
4
comment Level sets of convex functions
I haven't fully thought this through, but maybe you can set up a correspondence between the curves $f^{-1}\{t\}$ and $f^{-1}\{t+\mathrm dt\}$ in the normal direction and compare the lengths of infinitesimal segments along those curves. I'd imagine you might be able to derive $\mathrm d\ell/\mathrm dt$ as some kind of integral involving the first and second derivatives of $f$.
Jul
4
awarded  Enlightened
Jul
3
comment proving $\mathrm e <3$
@user946850, I consider $e = \sum_{n=0}^\infty 1/n!$ itself to be one of the many equivalent definitions of $e$.
Jul
3
awarded  Nice Answer
Jul
3
answered proving $\mathrm e <3$
Jul
3
comment Condition to have unique solution.
For future reference, you should write the operators as \Delta and \nabla instead of \triangle and \triangledown.
Jul
3
revised Condition to have unique solution.
deleted 6 characters in body
Jul
3
comment Direct proof that $\pi$ is not constructible
@Dave, your memory is not playing tricks on you. Your previous comment was on a now-deleted answer.
Jul
3
comment Ball from platform with specific vertex
@Joe: Yes, exactly. Either (1) or (2) will give you the value of $v_y$, but in general their answers will be different, which is why you can't fix both $H$ and $D$ independently. You still need (3) to get the value of $v_x$ after you have $v_y$.
Jul
3
comment Ball from platform with specific vertex
Now your solution is inconsistent. You're trying to choose all three of $\tan\alpha$, $v_y$, and $v_x$ independently, which doesn't make sense because $\tan\alpha$ has to be $v_y/v_x$.
Jul
3
comment Ball from platform with specific vertex
I don't think you're satisfying the condition that the ball must land at a distance $d$. (This is not the same as the condition that the ball achieves its maximum height at $x$-coordinate $d\frac D{100}$.)
Jul
3
comment Ball from platform with specific vertex
@JoeBlow, the explanation can't have been that superb if it didn't get my point across! I've edited the answer. In general, there is no solution that satisfies all your requirements.
Jul
3
revised Ball from platform with specific vertex
added 560 characters in body