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

I think four points is sufficient to find the location of the peak (but I've failed to figure out how in my tired state), and
I'm pretty sure a fifth point is necessary to find the height of the peak (since we don't know the radius of the mountain).

Of course, the above is rather useless without being able to back it up. The purpose of this post is really to provide the drawing I've been using (in part) while trying to figure out the solution. ABCD is the grid you presented, and P is the peak the mountain.

Update: Struck out what I realize I really do not know. There is definitely at least one case where the four points is insufficient to determine the height (when they are all at the same height), but that's all I know.

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

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Re^2: OT:Math problem: Grids and conical sections. by BrowserUk (Patriarch) on Nov 24, 2005 at 09:28 UTC
Thanks for the online sketch. I've a about 20 sheets of paper covered with similar sketches, but no way to display them. In the case of the 4 heights being equal, the peak will be centered, and a fifth spot reading there will determine the height. More generally, if the x & y can be calculated, then a fifth reading will retrieve the height directly. 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]

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Re^2: OT:Math problem: Grids and conical sections.
by BrowserUk (Patriarch) on Nov 24, 2005 at 09:28 UTC

Thanks for the online sketch. I've a about 20 sheets of paper covered with similar sketches, but no way to display them.

In the case of the 4 heights being equal, the peak will be centered, and a fifth spot reading there will determine the height. More generally, if the x & y can be calculated, then a fifth reading will retrieve the height directly.

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]