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[vagel7]

He simply made a calculation error at the very end. 3x / 4 = 9 / 2 is actually 6x = 36. Now it is correct.

[Bauglir]

Okay here's are two questions I mostly want confirmation of to make sure I don't spend a while implementing code that correctly does something, but which isn't actually what I want done.

Let's say I have two continuous curves, a and b, in the xy plane, defined between x₀ and x₁. For each curve, x₀ is either a maximum or a minimum, and x₁ is the other, and between the two neither dy/dx nor dx/dy is ever 0 (although it may be 0 at one of those two locations).

First, does this mean that for a given curve, y is either always increasing or always decreasing? That is to say, it never peaks in between the relevant xs.

Second, assuming that's the case, the two curves intersect if, and only if, the sign of y_a-y_b is different at x₀ and x₀, right? For the sake of argument, 0 is a different sign from + or - since it means an intersection at an endpoint.

[Vector]

You're correct on both points.

(hohohohoho)

[Bauglir]

Yesssssss. Now I just need to grok this in order to split everything where my assumptions aren't correct into cases where they are, and everything should be peachy. Soon, I will venture forth into the code mines! I'll have to hug the friend who randomly suggested this forever.

Thank you, Vector, for being awesome.

EDIT: Or maybe I don't even need to use the linked algorithm. Huh. Hehehehehe

[MagmaMcFry]

Second, assuming that's the case, the two curves intersect if, and only if, the sign of y_a-y_b is different at x₀ and x₁, right?

Hold up, here's a mistake. The "if" part is true, but the "only if" part is not. Simple counterexample here.

[Vector]

Oh, whoops.  I knew I wasn't looking at that closely enough ._.  Thanks for the catch, Fry...

[Furtuka]

[Bauglir]

Oh, balls. Hrrrrrrrm. Well, good thing I hadn't started writing code yet. That's probably why all the suggestions I've seen for what I want to do are so much more computationally expensive and difficult to grasp. Thanks!

[Skyrunner]

What is S() in the answer Wolfram Alpha gives for the integral of sin(x^2) ?

[da_nang]

What is S() in the answer Wolfram Alpha gives for the integral of sin(x^2) ?

Says it's the Fresnel S integral.

[da_nang]

Spoiler: Something along these lines, I take it? (click to show/hide)

[MagmaMcFry]

Spoiler (click to show/hide)

IIRC the gradient test is dm/dy = dn/dx, dm/dz = dp/dx, dn/dz = dp/dy.

Now grad(f) = {df/dx, df/dy, df/dz} = {m, n, p},  so f = ∫mdx + c₁(y, z) = ∫ndy + c₂(x, z) = ∫pdz + c₃(x, y). In this case, the function f(x, y, z) = 1/sqrt((x-a)²+(y-b)²+(z-c)²) satisfies these equations.

[Furtuka]

Spoiler: What am I doing wrong here? Am I suppose to set Dx Dy Dz to something? If so, to what? (click to show/hide)

[da_nang]

Spoiler: What am I doing wrong here? Am I suppose to set Dx Dy Dz to something? If so, to what? (click to show/hide)

Seems to me program isn't evaluating the derivatives. The answer would be correct if they did. Is there a simplify function? Or check if Dx, Dy, Dz are interpreted as something else.

[Pnx]

Quick question, is there some sort of formulaic or algebraic way to find when a factorial is greater than some number?

Like I want to find for example when N! > 100, I know I can find the answer by just plugging in values for N until I get a number greater than 100. But I was wondering if there was a better way.