lld,[=-aa~'jIR'i~l,z:-]ii~lilzr Dirk Huylebrouck, Editor J f you follow the summer crowd of square used to be an inn. High up on the I tourists biking along the Danube, you front wall, a plaque: on October 30, Kepler in may discover, close to Linz, a short de- 1613, the astronomer Johannes Kepler tour leading through shady woods to celebrated here his marriage to Susanne Eferding. This is a quiet little Upper Reuttinger, the daughter of a burgher Eferding Austrian town, offering the usual sight- from Eferding. seems' fare: castle, church, and market- By then, Kepler was a widower of Karl Sigmund place. The first house on the main 42. Born and raised in Wiirttemberg, he Does your hometown have any mathematical tourist attractions such as statues, plaques, graves, the cafd where the famous conjecture was made, the desk where the famous initials are scratched, birthplaces, houses, or memorials? Have you encountered a mathematical sight on your travels? If so, we invite you to submit to this column a picture, a description of its mathematical significance, and either a map or directions so that others may follow in your tracks. Please send all submissions to The Keplerhof Inn (formerly The Lion) on the main square of Eferding and the plaque com- Mathematical Tourist Editor, memorating Kepler's wedding. The house, which is well over five hundred years old, has lately Dirk Huylebrouck, Aartshertogstraat 42, become derelict and will probably be taken over by a bank. Encased in one of its walls is the 8400 9 Belgium tombstone of a Jewish refugee from Regensburg who had found shelter in Eferding in the e-mail: dirk.huylebrouck@ping,be year 1410. 9 2001 SPRINGERWERLAG NEW YORK, VOLUME 23, NUMBER 2, 2001 47 Measuring barrel contents. The left barrel is measured in the Austrian way, by help of a gauging rod. The other barrel's volume is deter- mined by pouring its content into vessels of specific volume. This is from the title page of a book on analysis, which appeared in 1980. Kepler in 1620, age forty-nine. According to his friend, the poet The drawing is from the title page of a treatise by Johann Frey, which Lansius, this is how Kepler did not look. Lansius jocularly put the was published in 1531 in Nuremberg. The formula (in white) is blame on the motion of the Earth (a heresy at that time, as Galileo Kepler's barrel rule. (From the cover of Analysis 1, 126, I.) came to learn): if the Earth had stood still, the artist's hand would have been steadier. had broken off his theological studies third law on planetary motion, was al- Susanne was seventeen years in Ttibingen to become professor of ready a celebrity in European science, younger than Kepler and seemed mod- mathematics at a college in Graz. Later, but this cut no ice with the suspicious est, thrifty, and devoted. He had met her he joined the astronomer Tycho Brahe farmers, who often chased him ignomi- in the household of a friend with a ring- in Prague, as one of the many scien- nously away from their land. ing name--Erasmus von Starhemberg-- tists, astrologers, and alchemists at- Having gone through an unhappy first whose palace dominated Eferding and tracted there by Rudolf II, the oddest marriage, Kepler took great pains to whose family popped up in every century of all Habsburg emperors, a dreamer avoid all mistakes on his second matri- of Austria's history. Erasmus had stud- suffering from fits of madness, who monial adventure. We know from a long ied in Strasburg, Padua, and Tfibingen, ended as a prisoner in his own castle. and almost comically candid letter where he may well have met young Kepler, who furnished his fair share of (dated from Eferding one week before Kepler for the first time. He was in sym- horoscopes, eventually held the job of his wedding and addressed to a scholarly pathy with Kepler's religious plight--a Imperial Mathematician under three nobleman) that he had wavered for two few years later, at the outbreak of the Habsburg rulers. Each was more nfili- years between no fewer than eleven can- Thirty Years War, he would himself be tantly Catholic than his predecessor, un- didates, among them a widow and her branded as a "main rebel" by the Catholic fortunately, and this made court life dif- daughter. Some were too young; some, establishment--and had arranged for ficult for Kepler, a staunch Protestant. too ugly. Some seemed inconstant, and Kepler's transfer to Linz. (Later, when After Rudolfs death, he took a second others lost their patience with his tem- Starhemberg was imprisoned, Kepler job as "district mathematician" in Linz. porising, which became the talk of the wrote to the Jesuit priest Guldin, a pro- This implied cartographical work, town. Eventually, Kepler decided for fessor at the University of Vienna and among other things. Kepler, by then number five, against the advice of all his no mean mathematician himself, to ask somewhere between his second and friends, who deemed her too lowly. him to intervene at the imperial court.) THE MATHEMATICAL INTELLIGENCER As for Susanne, she was an orphan: she The fact that their content was mea- lish the leaflet--at that time, an oner- had no money, but on the other hand, sured by more complicated means in ous enterprise that required, for no in-laws either. She was a ward of other countries, for instance on the starters, buying the necessary reams of Baron Erasmus's wife Elisabeth, who Rhine, rendered him suspicious. But a paper. Actually, Kepler had even to patronized an institution for the up- few days sufficed to convince him of convince a printer, first, to set up shop bringing of impoverished young ladies. the validity of what he termed the in Linz. The inevitable delays, which After having taken the plunge, Kepler Austrian method. He wrote a short took almost two years, offered him the never mentioned his spouse again in all note, and dedicated it, as a New Year's opportunity to extend his results con- his copious correspondence, except on gift, to Maximilian von Liechtenstein siderably. His Nova stereometria do- the seven occasions when she gave and Helmhard Jhrger, two of his gen- liorum vinariorum grew to a full- birth. Based on this, all biographers erous supporters. He next tried to pub- fledged book. The first part deals with agree that the marriage indeed was a happy one. The Eferding wedding plays a curi- ous role in the prehistory of calculus. In Kepler's words: After my remarriage in November of last year, at a time when barrels of wine from Lower Austria were stored high on the shores of the Danube near Linz after a copious vintage, on offer for a reasonable price, it was the duty of the new hus- band and devoted family-head to purchase the drink needed for his household. Four days after several barrels had been brought to the cel- lar, the wine-seller came with a rod which he used to measure the con- tent of all barrels, irrespective of their form and without any further reckoning or computation. The metallic end of the gauge-rod was introduced through the bung-hole till it reached the opposite point on the border of the barrels's bottom. 9 I was amazed that the diagonal through the half-barrel could yield a measure for the volume, and I doubted that the method could work, since a much lower barrel with a somewhat broader bottom and hence much less content could have the same rod-length. To me as a newlywed, it did not seem inop- portune to investigate the mathe- matical principle behind the preci- sion of this practical and widespread Title page of the Nova Stereometria. When well-meaning experts told Kepler that a mathe- measurement, and to bring to light matical text, and in Latin at that, would never find buyers, he produced a German version the underlying geometrical laws. (The Art of Measurement of Archimedes), which appeared in 1615 and must be one of the first examples of popular science writing: it was considerably shorter than the Stereometria, Posterity did not record what Susanne written in down-to-earth language, and divested of most proofs. Kepler also wrote the first made out of this. science fiction ever, an account of a voyage to the moon. He decided not to publish the in- Kepler, whose father had been an tegral text of his "Dream" during his lifetime, but it raised rumors of black magic which sur- innkeeper when not abroad as a soldier faced during the nearly fatal witchcraft trial that his mother had to undergo in her last years 9 of fortune, must have been on familiar Kepler seems to have been the first to see science as the cumulative effort of successive terms with wine-casks of all shapes. generations. VOLUME 23, NUMBER 2, 2001 49 cubatures in general, and in particular But the content of his book was not at and the circle's center for a vertex, has with the volumes of solids of revolu- all classical. In a remarkable display of the same area as the circle. The same tion. The second part deals with bar- intuition, he anticipated parts of calcu- works for the full sphere: it is made up rels. For Kepler, these were sometimes lus, arguing about infmities with a non- of infinitely many pyramids whose ver- cylinders, sometimes they consisted of chalance quite foreign to the rigor of the tices meet in the center; their bases re- two trunks of a cone, and sometimes exhaustion method of Archimedes (who duce to points on the surface of the they were what he termed "lemons" is invoked a great deal).