If you have a grid square of a map, and somewhere within that grid square you know there is the peak of a hill or mountain. You know the spot heights at each of the four corners of the grid. You don't know the height or position of the peak.

Update:The size of the grid is known, but is measured in different units to the spot heights and the relationship between the units is unknown. 

 566 +-----------+ 124
     |           |
     | .?        |
     |           |
     |           |
     |           |
 124 +-----------+ 100

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If you assume that the mountain is perfectly conical, with an even but unknown gradient all around it's perfectly circular slopes; is it possible to calculate:

  • the subgrid coordinates of the peak's position?
  • the peak's height?

    If not, would having an additional spot height either at the mid position of the grid, or the mid positions of the side of the grid square facilitate the calculations?

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    In reply to OT:Math problem: Grids and conical sections. by BrowserUk

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