Re^2: OT:Math problem: Grids and conical sections.

~~I don't recognize your equation for the cone because you've introduced a variable z without explaining what it is. You also are missing necessary square roots.~~

You can't just set the slope at 1 because the slope has a complex effect on the observed heights. Doing that massively simplifies the answer.

Those two math errors are significant enough that I see no reason to analyze farther.

Update: BrowserUk pointed out where the equation came from. Indeed it did not need square roots. However the slope definitely matters.

Comment on Re^2: OT:Math problem: Grids and conical sections.

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Re^3: OT:Math problem: Grids and conical sections. by BrowserUk (Patriarch) on Nov 24, 2005 at 21:52 UTC
I don't recognize your equation for the cone because you've introduced a variable z Isn't jeffguy's cone equation a reordering of equation 5 on this Wolfram page? Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error. Lingua non convalesco, consenesco et abolesco. -- Rule 1 has a caveat! -- Who broke the cabal? "Science is about questioning the status quo. Questioning authority". In the absence of evidence, opinion is indistinguishable from prejudice.	[reply]
Re^4: OT:Math problem: Grids and conical sections. by tilly (Archbishop) on Nov 25, 2005 at 02:07 UTC
Oh, so THAT's where he got it from. But he still can't just assume that the slope is 1. Let's take a concrete example and run a sanity check to demonstrate that. peak (1/2, 1/2), height 5, slope 2 point 1: bottom left 5 - 2sqrt((3/2)2 + (3/2)2) = 0.757359312880715 point 2: bottom right 5 - 2sqrt((1/2)2 + (3/2)2) = 1.83772233983162 point 3: top right 5 - 2sqrt((1/2)2 + (1/2)2) = 3.58578643762691 point 4: top left 5 - 2sqrt((3/2)2 + (1/2)2) = 1.83772233983162 a = 1.83772233983162 - 3.58578643762691 = -1.74806409779529 b = 0.757359312880715 - 3.58578643762691 = -2.8284271247462 c = 1.83772233983162 - 3.58578643762691 = -1.74806409779529 x = a(c-b)(a-c-b)/(4(a+c-b)) = -1.74806409779529 * (-1.74806409779529 - -2.8284271247462) * (-1.74806409779529 + -1.74806409779529 - -2.8284271247462) /( 4 * (-1.74806409779529 + -1.74806409779529 - -2.8284271247462) ) = -0.472135954999583 [download] and I'm not going to bother working out what he thinks that y should be since his value for x is already obviously wrong.	[reply] [d/l]
Re^3: OT:Math problem: Grids and conical sections. by jeffguy (Sexton) on Nov 25, 2005 at 02:05 UTC
You're right. At first glance, this looked like a term that wouldn't matter because of symmetry. For what it's worth, Z was the term representing the adjusted height of the peak (after subtracting the top-left corner off). Oh well -- back to math!	[reply]