The Goldeye fish has cycloid scales that lack spines. The cycloid, epicycloids, and hypocycloids have the property that each is similar to its evolute. The parametric representation formula 50 describes a cycloid. Most have smooth and overlapping ganoid, cycloid or ctenoid scales. Its body was covered by cycloid scales. The curve ZVA is a cycloid and CHV is its generating circle. These are the parametric equations for a cycloid. Consider the rectangle bounding a single cycloid arch. Their scales may be cycloid or ctenoid. The tautochrone curve is related to the brachistochrone curve, which is also a cycloid. The scales are relatively large, cycloid (smooth), and easily detached. Leptoid scales come in two forms&colon; cycloid and ctenoid. Therefore, he concludes that the minimum curve must be the cycloid. Several curves are related to the cycloid. The cycloid psychosis has a long history in European psychiatry diagnosis.