Reloj humedo


The rotation of the temporal cycles is shown in this work by Orozco. There is a wristwatch placed on a flat surface, which projects its shadow. The moisture on the surface of the watch dial is split into small droplets of water. The shadow and the watch form the symbol of a LEMNISCATE. Although the name LEMNISCATE dates to the late 17th century, the consideration of curves with this shape can be traced back to Proclus, a Greek Neoplatonist philosopher and mathematician who lived in the 5th century AD. Proclus considered the cross-sections of a torus by a plane parallel to the axis of the torus. As he observed, for most such sections the cross-section consists of either one or two ovals; however, when the plane is tangent to the inner surface of the torus, the cross-section takes on a figure like Orozco’s watch shadow, which Proclus called a horse fetter. The Greek phrase for a horse fetter became the word hippopede, the name for this shaped curve, which is also called the LEMNISCATE of Booth.

Cassini studied a family of curves where the locus of all points, the product of whose distances from two fixed points, the curves' foci, is a constant. Under very particular circumstances (when the half-distance between the points is equal to the square root of the constant) this gives rise to a LEMNISCATE.

In 1694, Johann Bernoulli studied the LEMNISCATE case of the Cassini oval, now known as the LEMNISCATE of Bernoulli. It is analytically described as the zero set of a polynomial equation in connection with a problem of "isochrones" that had been posed earlier by Leibniz.