ABSTRACT
The celestial body of Dürer's engraving Melencolia I is connected with his painting of a meteor, the Raveningham-painting; it is shown that the origin of this painting owns to the impact of the meteor of Ensisheim in 1492. Until now the celestial body, the balance, and the magic square are nearly consistently interpreted as the planet Saturn, the zodiac sign Libra, and the planet Jupiter, and the melancholy woman is subject to these heavenly bodies. Consequently, neoplatonic astrology has been the main focus of the engraving; including the rainbow, the engraving has also been interpreted biblically. The present paper, however, places emphasis on problems of the geometry as the reason of melancholy. Any astronomical meaning of the configuration of the numbers of the magic square is discarded.
Subject(s)
Astronomical Phenomena , Depressive Disorder/history , Engraving and Engravings/history , Medicine in the Arts , Meteoroids , Female , Germany , History, 16th Century , HumansABSTRACT
A spin-dimer analysis of the anisotropic spin-exchange interactions in the distorted wolframite-type oxides CuWO4, CuMoO4-III, and Cu(Mo(0.25)W(0.75))O4 was performed by Koo and Whangbo (Inorg. Chem. 2001, 40, 2161-2169). For Cu(Mo(0.25)W(0.75))O4, a magnetic structure with a magnetic unit cell doubled along the a and b axes has been predicted, but neutron powder diffraction on Cu(Mo(0.25)W(0.75))O4 did not confirm such a magnetic structure. In the present work, a detailed spin-dimer analysis, considering the influence of particular atomic structure parameters, finally revealed that a wrong coordinate transformation of the Cu z coordinate of the Cu(Mo(0.25)W(0.75))O4 structure is responsible for the prediction of the new, hypothetical magnetic structure. The deviation from the correct value is too small to be recognized by unreasonable bond lengths or angles but is sufficient to change one specific calculated value that is responsible for the prediction of the hypothetical magnetic structure.
ABSTRACT
New mathematical hypotheses are postulated concerning the truncated rhombohedron in Dürer's engraving Melencolia.I as well as the relation of the rhombohedron to the magic square. The two free parameters of a truncated rhombohedron have to be chosen in a way that (i) its front orthogonal elevation is nearly quadratical and with the form of the magic square, and that (ii) it possesses approximately a circumscribed sphere. Both conditions result in a value of 79.2 degrees for the angle of the rhombohedron. Measuring two lengths of the rhombohedron of the engraving yields the same value. In the magic square, the numbers are positioned in a way that the connection lines between four numbers give the sum 34 for lines which are the projection lines of the edges of the rhombohedron. In the Nürnberg-Codex of Dürer's manuscripts, exists a page with some sketches of mostly archimedean solids. One sketch represents a pentagon with approximately the measures of the six lateral faces of the truncated rhombohedron. It has to be looked upon as a preliminary sketch for the solid of the engraving. In 1543 Augustin Hirschvogel from Nürnberg, as the next after Dürer, rediscovered a further archimedean solid; this rediscovering has been attributed to D. Barbaro until now.
