Editing Johannes Kepler (section)

== Mathematics and physics ==
[[File:Kepler conjecture 1.jpg|thumb|upright=.9|A diagram illustrating the [[Kepler conjecture]] from ''Strena Seu de Nive Sexangula'' (1611)]]
As a New Year's gift that year (1611), he also composed for his friend and some-time patron, Baron Wackher von Wackhenfels, a short pamphlet entitled ''Strena Seu de Nive Sexangula'' (''A New Year's Gift of Hexagonal Snow''). In this treatise, he published the first description of the hexagonal symmetry of snowflakes and, extending the discussion into a hypothetical [[atomism|atomistic]] physical basis for their symmetry, posed what later became known as the [[Kepler conjecture]], a statement about the most efficient arrangement for packing spheres.<ref>Schneer, "Kepler's New Year's Gift of a Snowflake," pp.&nbsp;531–545</ref><ref>{{Cite book |last1=Kepler |first1=Johannes |editor1-last=Hardie |editor1-first=Colin |editor-link=Colin Hardie |title=De nive sexangula |trans-title=The Six-sided Snowflake |date=1966 |orig-year=1611 |publisher=Clarendon Press |location=Oxford |oclc=974730 }}</ref> This was proved in 1998 by [[Thomas Callister Hales]].<ref>{{Cite journal |last=Hales |first=Thomas C. |date=2006 |title=Historical Overview of the Kepler Conjecture |url=http://link.springer.com/10.1007/s00454-005-1210-2 |journal=Discrete & Computational Geometry |language=en |volume=36 |issue=1 |pages=5–20 |doi=10.1007/s00454-005-1210-2 |issn=0179-5376}}</ref>

Kepler wrote the influential mathematical treatise ''Nova stereometria doliorum vinariorum'' in 1613, on measuring the volume of containers such as wine barrels, which was published in 1615.<ref>Caspar, ''Kepler'', pp.&nbsp;209–220, 227–240. In 2018 a complete English translation was published: ''Nova stereometria doliorum vinariorum / New solid geometry of wine barrels. Accessit stereometriæ Archimedeæ supplementum / A supplement to the Archimedean solid geometry has been added''. Edited and translated, with an Introduction, by [[Eberhard Knobloch]]. Paris: Les Belles Lettres, 2018. {{ISBN|978-2-251-44832-9}}</ref> Kepler also contributed to the development of infinitesimal methods and numerical analysis, including iterative approximations, infinitesimals, and the early use of logarithms and transcendental equations.<ref>{{Cite journal|last=Belyi|first=Y. A.|date=1975|title=Johannes Kepler and the development of mathematics|url=https://www.sciencedirect.com/science/article/abs/pii/008366567590149X|journal=Vistas in Astronomy|language=en|volume=18|issue=1|pages=643–660|doi=10.1016/0083-6656(75)90149-X|bibcode=1975VA.....18..643B}}</ref><ref>{{Cite journal|last=Thorvaldsen|first=S.|date=2010|title=Early Numerical Analysis in Kepler's New Astronomy|url=https://www.cambridge.org/core/journals/science-in-context/article/abs/early-numerical-analysis-in-keplers-new-astronomy/0E28ED84C5D50F003537FCB2C97B31D0|journal=Science in Context|language=en|volume=23|issue=1|pages=39–63|doi=10.1017/S0269889709990238|s2cid=122605799}}</ref> Kepler's work on calculating volumes of shapes, and on finding the optimal shape of a wine barrel, were significant steps toward the development of [[calculus]].<ref>{{Cite web |last=Cardil |first=Roberto |date=2020 |title=Kepler: The Volume of a Wine Barrel |url=https://www.maa.org/book/export/html/117621 |access-date=16 July 2022 |website=Mathematical Association of America}}</ref> [[Simpson's rule]], an approximation method used in [[integral calculus]], is known in German as ''Keplersche Fassregel'' (Kepler's barrel rule).<ref>{{Cite journal |last=Albinus |first=Hans-Joachim |date=June 2002 |title=Joannes Keplerus Leomontanus: Kepler's childhood in Weil der Stadt and Leonberg 1571&ndash;1584 |journal=The Mathematical Intelligencer |language=en |volume=24 |issue=3 |pages=50–58 |doi=10.1007/BF03024733 |s2cid=123965600 |issn=0343-6993|doi-access=free }}</ref>