Perfect balance: Difference between revisions
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A non-empty finite set of real numbers ''S'' in the range <math>[0, 1)</math> is called '''perfectly balanced''' if a wheel with an equal weight placed at angle <math>2\pi x</math> for each <math>x \in S</math> has its center of gravity exactly at the hub. Mathematically, this is given by the equation <math>\sum_{x \in S} e^{2\pi i x} = 0</math>. | A non-empty finite set of real numbers ''S'' in the range <math>[0, 1)</math> is called '''perfectly balanced''' if a wheel with an equal weight placed at angle <math>2\pi x</math> for each <math>x \in S</math> has its center of gravity exactly at the hub. Mathematically, this is given by the equation <math>\sum_{x \in S} e^{2\pi i x} = 0</math>. | ||