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    Standard Tori

    Definition

    One of the three classes of tori illustrated above and given by the parametric equations x | = | (c + a cos v) cos u y | = | (c + a cos v) sin u z | = | a sin v. The three different classes of standard tori arise from the three possible relative sizes of a and c. c>a corresponds to the ring torus shown above, c = a corresponds to the horn torus which touches itself at the point (0, 0, 0), and c