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Johannes Kepler in Ulm Revisited: New Aspects of Old Known Facts—

A Tribute in Honor of Kepler’s 450th Birthday

  • The Mathematical Tourist
  • Ma. Louise Antonette De Las Peñas, Editor
  • Published:
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Notes

  1. Louis Poinsot (1777–1859) found the other two of the four nonconvex regular polyhedra.

  2. Kepler’s mother, Katharina, was accused of witchcraft in Leonberg in 1620, which led to a lengthy trial, resulting in first-degree torture; thanks to Johannes Kepler’s tireless efforts, the legal proceedings ended in an acquittal [41].

  3. Published only in 1713, in Jacob Bernoulli’s (1654–1705) posthumous Ars Conjectandi.

  4. In English: two feet my depth, one ell across • one well-calibrated bucket empties me • then three and a half centners will remain • full of Danube water : : I weigh seven • but you’d do better with grain • if you empty me sixty-four times • you will have wealth of ninety imes • Hans Braun cast me in 1627.

  5. Kanones pueriles, i.e., rules for children, that is, irrelevant or foolish rules, is an anagram of Ioannes Keplerus. There are more such anagrams on the title page, e.g., Kleopas Herennius for Iohannes Keplerus; see Figure 7.

  6. The most famous of Kepler’s distichs is probably his own epitaph: Mensus eram coelos, nunc terrae metior umbras. Mens coelestis erat, corporis umbra iacet (I have measured the heavens, now I measure the shades of the earth. While my mind was directed at heaven, here lies the shade of my body).

  7. The authors would be grateful for any hint that leads to the solution of this riddle!

  8. Albrecht Wenzel Eusebius von Wallenstein (1583–1634), Duke of Friedland (from 1625), Prince of Sagan (from 1628), Duke Albrecht VIII of Mecklenburg (from 1629) was general field marshal of the Catholic League during the Thirty Years’ War.

  9. Schad became a councilor in 1610, held many municipal official duties, and was, among other things, a supervisor of the armory and guns, churches, monasteries, and schools. In 1623, he was elected to the Secret Council; he represented Ulm on numerous imperial, county, city, and Protestant Union meetings.

  10. Also called horoscopus, i.e., the point of the ecliptic within a zodiacal sign that rises in the sky in the east of the considered place and at the exact time of the event considered (e.g., birth), as the second most important element after the zodiacal sign of the day of the event.

  11. The writing was a New Year’s gift (strena) for a friend, the lawyer and imperial councilor Johann Matthäus Wacker von Wackenfels (1550–1619). Kepler discovered that snow crystals, a collection of many water molecules, always form hexagonal patterns (as a direct consequence of the triatomic molecular structure of the water). This symmetry is maintained when several crystals attach to each other. Kepler also makes observations in the direction of crystalline structures and an atomic structure of matter, according to his understanding of the harmony of the world. The atoms of gold, silver, and platinum, for example, are actually arranged as optimal surface-centered cubic lattice sphere packings [55].

  12. The authors would be grateful for any information on the relief.

  13. The University of Graz was founded in the course of the Counter-Reformation as a Jesuit Catholic university in 1586. Kepler could not live in accordance with his Protestant faith there. The University of Linz was founded only in 1962.

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  1. Alter Bahnhofsweg 4, 71229, Leonberg, Germany

    Hans-Joachim Albinus

  2. Auf der Höhe 26, 59427, Unna, Germany

    Detlef Suckrau

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Correspondence to Hans-Joachim Albinus.

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Albinus, HJ., Suckrau, D. Johannes Kepler in Ulm Revisited: New Aspects of Old Known Facts—. Math Intelligencer 43, 64–77 (2021). https://doi.org/10.1007/s00283-021-10042-4

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