MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

Biographical Vignettes 155
[105]. As a devout Lutheran, he enrolled at the University of Tübingen in 1589
as a student of theology but also studied mathematics and astronomy under
Michael Mästlin, one of the leading astronomers of the time, who converted
him to the Copernican view of the cosmos. At the end of his university studies
in 1594, he abandoned his plans for ordination (in fact, he was excommunicated
in 1612) and accepted a post teaching Mathematics in Graz. In 1596,
he published Mysterium cosmographicum where he put forth a model of the
solar system based upon inscribing and circumscribing each of the five Platonic
solids by spherical orbs. On this basis, he moved to Prague in 1600 as Tycho
Brahe’s mathematical assistant and began work on compiling the Rudolphine
Tables. In 1601, upon Tycho’s death, he succeeded him as Imperial Mathematician
and the next eleven years proved to be the most productive of his life.
Kepler’s primary obligations were to provide astrological advice to Emperor
Rudolph II and to complete the Rudolphine Tables. In 1604, he published
Astronomiae pars optica where he presented the inverse-square law governing
the intensity of light, treated reflection by flat and curved mirrors and elucidated
the principles of pinhole cameras (camera obscura), as well as considered
the astronomical implications of optical phenomena such as parallax and the
apparent sizes of heavenly bodies. He also considered the optics of the human
eye, including the inverted images formed on the retina. That same year, he
wrote of a “new star” which is today called Kepler’s supernova. In 1609, he
published Astronomia nova where he set out his first two laws of planetary
motion based upon his observations of Mars. In 1611, he published Dioptrice
where he studied the properties of lenses and presented a new telescope design
using two convex lenses, now known as the Keplerian telescope. That same
year, he moved to Linz to avoid religious persecution and, as a New Year’s gift
for his friend and sometimes patron Baron von Wackhenfels, published a short
pamphlet, Strena Seu de Nive Sexangula, where he described the hexagonal
symmetry of snowflakes and posed the Kepler Conjecture about the most efficient
arrangement for packing spheres. Kepler’s Conjecture was solved only
after almost 400 years by Thomas Hales [301]! In 1615, he published a study
of the volumes of solids of revolution to measure the contents of wine barrels,
Nova stereometria doliorum vinariorum, which is viewed today as an ancestor
of the infinitesimal calculus. In 1619, Kepler published his masterpiece, Harmonice
Mundi, which not only contains Kepler’s Third Law, but also includes
the first systematic treatment of tessellations, a proof that there are only thirteen
Archimedean solids (he provided the first known illustration of them as
a set and gave them their modern names), and two new non-convex regular
polyhedra (Kepler’s solids). In 1624 and 1625, he published an explanation
of how logarithms worked and he included eight-figure logarithmic tables with
the Rudolphine Tables which were finally published in 1628. In that year, he
left the service of the Emperor and became an advisor to General Wallenstein.