Watt's Linkage
When the curve crosses the origin, the origin is a point of inflection and therefore has contact of order 3 with a tangent. However, if a2=b2+<c2 then tangent has contact of order 5 with the tangent, in other words the curve is a close approximation of a straight line. This is the basis for Watt's linkage.
Read more about this topic: Watt's Curve
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“Herein is the explanation of the analogies, which exist in all the arts. They are the re-appearance of one mind, working in many materials to many temporary ends. Raphael paints wisdom, Handel sings it, Phidias carves it, Shakspeare writes it, Wren builds it, Columbus sails it, Luther preaches it, Washington arms it, Watt mechanizes it. Painting was called “silent poetry,” and poetry “speaking painting.” The laws of each art are convertible into the laws of every other.”
—Ralph Waldo Emerson (1803–1882)