Re^3: OT:Math problem: Grids and conical sections.

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?

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Comment on Re^3: OT:Math problem: Grids and conical sections.

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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]

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Re^4: OT:Math problem: Grids and conical sections.
by tilly (Archbishop) on Nov 25, 2005 at 02:07 UTC

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 - 2*sqrt((3/2)**2 + (3/2)**2)
    = 0.757359312880715
point 2: bottom right
  5 - 2*sqrt((1/2)**2 + (3/2)**2)
    = 1.83772233983162
point 3: top right
  5 - 2*sqrt((1/2)**2 + (1/2)**2)
    = 3.58578643762691
point 4: top left
  5 - 2*sqrt((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]

[reply]
[d/l]