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Apr
22
comment Why do folded concentric circles and rectangles form a hyperbolic paraboloid?
@KyleKanos Origami would tell you how to make it, not why it folds the way it does. The solution clearly lies in analyzing what internal forces and stresses in the paper are created by the folds and bending, which is pretty squarely in physics territory.
Apr
17
answered How to tell if points in $Z^2$ belong to a half-plane?
Apr
11
awarded  Yearling
Apr
11
answered $A \oplus C = B \oplus C$ but $A\neq B$
Apr
6
comment Sketch the graph of the polynomial function $P(x)= x(x-3)(x+2)$
Your intervals have their ends at each of the roots. These are $-2, 0,$ and $3$. So yes, $x=0$ should be included as a boundary and you should test on either side of it to figure out whether the polynomial is positive or negative there.
Apr
6
comment Calculus on manifolds
It's tedious in comparison. You can do it (by 'it' I mean set up an appropriate surface integral, not direct integration in $\mathbb{R}^3$ which doesn't work as Nicholas has pointed out), but you end up doing all the intrinsic calculations anyway. Adding other calculations and things to look out for on top of that doesn't make life easier in the long run.
Apr
6
answered Sketch the graph of the polynomial function $P(x)= x(x-3)(x+2)$
Mar
22
answered Intuitive idea of axiom of choice
Mar
18
comment Application of Composition of Functions: Real world examples?
A function is just a process that turns one thing into another thing. Anytime you're describing something that chains processes together one after the other you're composing functions. You find a probability distribution and then want to find its average. Find a particle's position as a function of time, and then its distance from its start point. Almost any time you want to do multiple things to a function you're composing it with other functions.
Mar
5
awarded  calculus
Feb
12
comment What are the practical applications of the Taylor Series?
@Ruslan you can use the symmetries and periodicity of $\sin(x)$ to restrict your calculation to $[0,\pi/2]$. It's this range that has the maximum error of $8\%$.
Feb
1
comment Are there any other purposes for variables in math other than functions?
@tazheneryduck0 No, that doesn't make any sense. If you divide by $x$ you need to know that any results you get are only okay if $x\neq 0$, because otherwise the division wasn't allowed. But you can definitely divide by variables to find solutions to equations, it's used all the time. Your teacher seems to be confused. If $x$ is a root then $f(x)$ is what ends up being zero. That doesn't prevent you from dividing by $x$ at all.
Jan
31
answered Are there any other purposes for variables in math other than functions?
Jan
28
comment Why are particular combinations of algebraic properties “better” (richer and more pervasive) than others?
While I don't have a full answer, I would like to point out that associativity is what allows you to move your focus around when solving equations. Commutative but non-associative operations only let you switch two things around, not several in a row, so you barely gain any freedom. Associativity without commutativity is much less restricting. Also function composition is associative, (regardless of formalism; any sensible definition would be) so any algebra that can be interpreted as a collection of transformations (which is a large number of them) has to be associative.
Dec
8
awarded  Nice Answer
Dec
3
comment Explaining probability theory versus statistics
Doesn't this assume that you can't take a Bayesian approach to statistics?
Nov
30
answered Nullspace that spans $\mathbb{R}^n$?
Nov
26
comment Proof that imaginary numbers exist?
Do you mean "exist" as in "part of the 'real world'"? Or do you mean "how do you prove that you can consistently add square roots of negative numbers in a logically consistent way"?
Nov
18
revised Parametric form of a plane
deleted 3 characters in body
Nov
18
comment Parametric form of a plane
@AndyG Yes, it seems it should be. I'll update, thanks