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The famous Belvedere Apollo at the top
This marble is now in the
The Burning Mirrows wall painting is from the Stanzino delle Matematiche in the Galleria degli Uffizi (Florence, Italy). Painted by Giulio Parigi (1571-1635) in the years 1599-1600.
Another attempt to solve one of the three famous construction problems from Antiquity.
Diocles is one of many mathematicians who have attempted to construct a cube whose volume is exactly twice that of a given cube. This is often called the "Delian" problem or "duplication of the cube".
The curve invented by Diocles in about 180 BC later appears in the works of Fermat, Roberval, Huygens, Wallis, Newton, and others. Problems on the cissoid's curvature, arc length, and areas bounded by its asymptote are found in modern calculus texts.
The cissoid also has much in common with the modern need to identify the focal point of a satellite "dish." The cissoid may be represented as the "Roulette for the Vertex of a Parabola", or the curve traced by a fixed point on a parabolic curve as that curve rolls without slipping along a second curve. Thus, if a fixed point on a parabola moves along a second parabola of similar dimensions, the vertex will become the cusp of a cissoid of Diocles. Moreover, if the cusp is taken as the inversion center, the cissoid inverts to a parabola.
Diocles investigated the properties of the focal point of a parabola in On Burning Mirrors. There is a similar title in the works of Archimedes. The problem, then as now, is to find a mirror surface such that when it is placed facing the sun, heat is produced. Legend suggests Archimedes wanted to use parabolic mirrors reflecting the sun's rays to burn the sails of enemy ships.
Today, experimental solar collectors near Barstow, California, focus the sun's rays on a central water tower where heat is converted to electricity.