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Advanced Math/Harvard-MIT Math Problem?


Can you explain this math problem to me? I have the explanation, but even that I do not understand. The question is

Does it have something to do with the complex plane? I'm confused about the explanation and have not learned this before.

Yes, this does have to do with the complex plane, at least in the fact that it uses complex numbers. However, its really more of a geometry and algebra problem.

Solution 1 is clever in that it recognizes that the Law of Cosines gives

x = a^2 + b^2 -2(ac)cosθ = a^2 + b^2 +ac when θ = 120 degrees, etc.

This then defines the point P inside the triangle ABC, as described. The solution then applies Heron's formula (never heard of it) to set up the rest of the equations.

Solution 2 is more how I would have tackled it, which is to say I would have used combinations of the 3 x, y, z equations to solve for ab + bc + ca as shown (I believe that "x = BC^2" should really be x = (BC)^2, etc.). The term "cyclic" just means that the companion equations for x - y, namely y - z and z - x, are defined similarly. The rest is "just" algebra.

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randy patton


college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography


26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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