Problems.cc
Interactive lesson: Minimum and Maximum Problems in Geometry
On Problems.cc you get the interactive explanation for this topic and curated problems to practise. That is the same training system we use between Exact Science lessons.
- Interactive explanation (demo or sandbox where we have one)
- Curated problems to practise, with hints and solutions
- Progress tracked between lessons
Opens on Problems.cc in a new tab
Theory
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Discussions on maximum/minimum and equilibrium in nature/geography.
Shortest distance problems:
- On a plane, consider a straight line l and points A and B on one side of it. Determine the point M on the straight line such that the sum of AM+BM is minimized.
- On a plane, there is a given straight line l and three points A, B, and C on one side of it. Identify the point M on the straight line for which the sum AM+BM+CM is minimized.
- Given a convex quadrilateral on a plane, find the point for which the sum of distances to its vertices is minimized.
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Fagnano's problem: For a given acute triangle determine the inscribed triangle of minimal perimeter.
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Fermat-Torricelli point: the sum of the three distances from each of the three vertices of the triangle to the point is the smallest possible or, equivalently, the geometric median of the three vertices.
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Sphere. Great-circle distance - understanding spherical distances.
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Conic sections: Definitions and focal properties of:
- circle
- ellipse
- parabola
- hyperbola
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Steiner tree problem. (*)