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Search Results for “Fagnano”

By Phil Todd
Minimum Perimeter Inscribed Triangle
Three masses are constrained to lie on the edges of a triangle.  Equal constant force actuators (with force F) are attached to each pair of masses.  When this system finds equilibrium, the potential energy will be at a minimum.  However, the PE in each actuator is simply F times L, where L is the length of the actuator. Hence minimum PE is achieved when the masses sit at the vertices of the minimum perimeter inscribed triangle. Press Show to see the normals to the sides of the triangle at the location of the masses.

Tags: Fagnano, altitude, triangle

By Phil Todd
Maximum Perimeter Triangle
Constant force actuators push outwards.  As the potential energy in each actuator is equal to its length, this machine should settle where the triangle's perimeter is maximum. Press Show to see the reflections in the tangents of a beam of light transmitted along one edge of the triangle.

Tags: maximum, Fagnano, perimeter

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