The Three-Point Problem in the Context of Elementary Vector Analysis

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Computer assisted instruction, engineering and environmental geology, geology teaching, hydrogeology and hydrology, problems - geomathematical, structural geology

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The classic three-point problem involves finding the attitude of an inclined plane from the elevation of the plane at three points. Development of an analytical solution for this problem from elementary vector analysis can be used as a teaching tool to clarify the fundamental relationships between (a) the mathematical concepts of gradient and partial and directional derivatives, and (b) the geologic concepts of strike and true and apparent dips. This approach to the three-point problem is helpful to hydrogeology students because it clarifies several mathematical concepts that are crucial to understanding and applying Darcy's Law. The analytical solution is also useful in lab exercises on groundwater flow because many cases can be calculated in a short time with a microcomputer. This allows the students to examine the effects of specific variables on the calculated magnitude and direction of ground-water flow; particularly instructive is a set of problems in which the three-point data are the same but the amount and direction of anisotropy are variable.

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Journal of Geological Education, v. 37, issue 4, p. 280-287