↑ The full title is Ioannis Keppleri Harmonices mundi libri V (The Five Books of Johannes Kepler's The Harmony of the World).
↑ Johannes Kepler, Harmonices Mundi [The Harmony of the World] (Linz, (Austria): Johann Planck, 1619), p. 189. From the bottom of p. 189: "Sed res est certissima extactissimaque quod proportio qua est inter binorum quorumcunque Planetarum tempora periodica, sit præcise sesquialtera proportionis mediarum distantiarum, id est Orbium ipsorum; … " (But it is absolutely certain and exact that the proportion between the periodic times of any two planets is precisely the sesquialternate proportion [i.e., the ratio of 3:2] of their mean distances, that is, of the actual spheres, … " An English translation of Kepler's Harmonices Mundi is available as: Johannes Kepler with E.J. Aiton, A.M. Duncan, and J.V. Field, trans., The Harmony of the World (Philadelphia, Pennsylvania: American Philosophical Society, 1997); see especially p. 411.
1 2 3 Field, J. V. (1984). A Lutheran astrologer: Johannes Kepler. Archive for History of Exact Sciences, Vol. 31, No. 3, pp. 207-219.
↑ Voelkel, J. R. (1995). The music of the heavens: Kepler's harmonic astronomy. 1994. Physics Today, 48(6), 59-60.
1 2 3 4 5 Brackenridge, J. (1982). Kepler, elliptical orbits, and celestial circularity: A study in the persistence of metaphysical commitment part II. Annals of Science, 39(3), 265.
↑ Cromwell, P. R. (1995). Kepler's work on polyhedra. Mathematical Intelligencer, 17(3), 23.
1 2 Schoot, A. (2001). Kepler's search for form and proportion. Renaissance Studies: Journal of the Society for Renaissance Studies, 15(1), 65–66.
↑ The opening of the film Mars et Avril, by Martin Villeneuve, is based on Kepler's cosmological model in Harmonices Mundi, in which the harmony of the universe is determined by the motion of celestial bodies. Benoît Charest also composed the score according to this theory. This opening sequence can be seen here: https://vimeo.com/66697472
↑ Walker, D. P. (1964). Kepler’s celestial music. Journal of the Warburg and Courtauld Institutes, Vol. 30, pp. 249.
