Ian Stewart*

The catapult that Archimedes built, the gambling-houses that Descartes frequented in his dissolute youth, the field where Galois fought his duel, the bridge where Hamilton carved quaternions-- not all of these monuments to mathematical history survive today, but the mathematician on vacation can still find many reminders of our subject's glorious and inglorious past: statues, plaques, graves, the cafd where the famous conjecture was made, the desk where the

famous initials are scratched, birthplaces, houses, memorials. Does your hometown have a mathematical tourist attraction? 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 mathe- matical significance, and either a map or directions so that others may follow in your tracks. Please send all submissions to the Mathematical Tourist Editor, Ian Stewart.

Sacred Star Polyhedron Istv n Hargittai

There is a beautiful star polyhedron at the top of the Sacristy of St. Peter's Basilica in Vatican City (Fig. 1). It was built by the architect Carlo Marchionni in the years

1776-1784. It is a great stellated dodecahedron, called also Kepler's great stellated dodecahedron (Fig. 2 [1]), wi th 2 of its 20 triangular pyramids left out to accom-

Figure 1. Left: The Sacristy of St. Peter's Basilica in Vatican City; right: the star polyhedron at its top.

*Column Editor's address: Mathematics Institute, University of Warwick, Coventry, CV4 7AL England.

5 2 THE MATHEMATICAL INTELLIGENCER VOL. 18, NO. 3 �9 1996 Springer-Verlag New York

modate the vertical rod serving as the stand of the cross above the polyhedron.

There are many other examples of star polyhedron decorations from even earlier times, such as at the top of the obelisks in St. Peter's Square and in the Rotonda Square in Rome, and on the gate in the Square of September 20 in Bologna (Fig. 3). The star polyhedron often stands on a pile of dome-shaped stones.

An octagonal star standing on top of a pile of dome- shaped stones was a characteristic motif in the coat of arms of the Chigi family of Pope Alexander VII (1655-1667). This motif is prominently displayed on the colonnades of St. Peter's Square (Fig. 4).

Giovanni Lorenzo Bernini (1598--1680) and Francesco Borromini (1599-1667) were leading architects of the Baroque period and their activities overlapped with the reign of Pope Alexander VII. The octagonal star and the coat of arms of the Chigi family are conspicuously pres- ent in many of their works. Figure 5 shows Sant Ivo's Church and three of its details by Borromini. Two of them display star polyhedra on piles of dome-shaped stones and octahedral stars. However, the decoration beneath the cross at the top of the tower is not a poly- hedron but a sphere.

All photographs in this article were taken by the au- thor in 1993. I am grateful to Anna Rita Campanelli and

Figure 2. Great steUated dodecahedron. Photograph courtesy of Magnus J. Wenninger [1].

Aldo Domenicano (Rome), Lodovico Riva di Sansev- erino (Bologna), and Magnus J. Wenninger (Collegeville, Minnesota) for assistance and advice.

Figure 3. Left: Top of the obelisk in St. Peter's Square, Vatican City; center: top of the obelisk in Rotonda Square, Rome; right: one of the two side decorations of the gate in the Square of September 20, Bologna.

THE MATHEMATICAL INTELLIGENCER VOL. 18, NO. 3 1996 53

R e f e r e n c e

1. M. J. Wenninger, Polyhedron Models, New York: Cambridge Universi ty Press (1971).

Budapest Technical University Szt. Gelldrt, tdr 4 I-I-1521 Budapest, Hungary

Figure 4. Decoration from the top of the colonnade in St. Peter's Square, Vatican City.

Figure 5. Sant Ivo 's Church (top right) wi th three detai ls enlarged (above).

THE MATHEMATICAL INTELLIGENCER VOL. 18, NO. 3, 1996 54

Simon Stevin's Statue

Dirk Huylebrouck

Simon Stevin was born in the Belgian city of Bruges in 1548, but left Belgium in 1582 and became a few years later professor of mathematics at the Universi ty of Leyden. A successful engineer, he first publ ished his mathematics in Latin (1583: Problemata Geometrica), but later defended the "use of the mother tongue to stimu- late the progress of science" (1585: Dialectike ofte Bewysconste, The Art of Proving Statements). He died in 1620. The Universi ty of Gent placed his bust in an au- ditorium, and until 1994 its mathematics review was named after him (see below).

Belgium-in-24-hour tourists always have on their pro- gram a visit to the Venice of the North, Bruges. From Brussels, there is only one way to drive th rough this city c rowded with tourists, and one cannot miss the Simon Stevin square in the centre of Bruges. A statue erected in his honor shows a thinking man, holding a pair of compasses in the right hand, and resting the left hand on a book with a drawing of a paral lelogram for adding forces. The inscription

S IMON STEVIN INAUG. MDCCCXLVI.F.

tells us it took the city more than 200 years to honor the mathematician. It was indeed quite a controversial de- cision. Until the first half of the 19th century, the Catholic Belgian and Protestant Dutch blocs were in- volved in something like a cold war, and to some Stevin had passed to the other side of the religious curtain. Several politicians and priests did not hesitate to use in- sults, but the offended par ty for tunately got the statue anyway.

The following plea in his favor by the (Belgian!) physi- cist A. Quetelet is more polite, a l though the ordinary peo-

ple he refers to include a member of the Brussels Academy of Science. Many of the statements may still be valid today (just replace "princes," "crusade," etc. by "generals," "war," etc. and use names you think ap- propr ia te instead of Simon Stevin and Bruges):

Simon Stevin, no matter what foreigners have said, was not forgotten by his compatriots. His statue will decorate his na- tive city and will make her proud, a pride he felt himself for her, since it was the only title he used in his works, on the front pages of which one reads the words so remarkable in their simplicity: "By Simon Stevin of Bruges'. But, one may say, does an ordinary scholar, whose name the ordi- nary people do not know, deserve the honor of a statue? Certainly! an ordinary scholar, who, lost in the mass of peo- ple, has grown by himself and the force of his genius up to the highest conceptions: who, by his work and his insight, impregnated the domain of the intelligence; who tore aside with a steady hand the veils covering the great laws of na- ture; who enriched us with useful discoveries whose fruits we reap peacefully: what, this scholar should not take place next to those great conquerors who distinguished them- selves, very often, by the evil they caused to humanity: those princes who impoverished and exterminated their popula- tion, and brought ruin and desolation to their neighbors?

If you deify those men, then do not deny the honors given to great virtues, to sublime intellects. Those precious qual- ifies are more obvious signs of Divinity than those you honor by your statues. It is in the obscurity of the forest, in the childhood of society that man, still under the strain of material compulsion, elevated fear and glorified him who inspired it. Today, our honors must see higher; and the na- tion that knows how to celebrate the great military virtues, who made a statue for the famous head of the first crusade, for the hero praised by Tasso; that nation will not refuse to use the talent of its sculptors to reproduce features of its children who distinguished themselves in other careers as well. If the ordinary people do not know their names, let them learn them; that they know who their benefactors were. Ingratitude is humiliating; it is one of the principal

THE MATHEMATICAL INTELLIGENCER VOL. 18, NO. 3 �9 1996 Springer-Verlag New York 5 5

factors of dissolution of societies: it breaks the links, fosters political egoism, and dries up the source of all the civic virtues.

Honor to the city of Bruges, which wanted to celebrate the memory of one of its most famous sons! More than one young talent will be roused before this monument of grat- itude, and even a foreigner will not look at it unmoved.

Before climbing, two centuries after his death, on the pedestal dest ined to him, the scholar of Bruges met more than one obstacle. Was not he even accused of bearing arms against his country? And on what proof was this accusation based? I do not know, and neither do those who made the accusations, because the life of Simon Stevin is clouded by mysteries; and al though the scholar held high functions, one only knows him through his works and by the few things he told us about himself in his works. But the silence of his- tory does not authorize us to become unjust twice towards him.

Q u e t e l e t ' s tex t is q u o t e d in A. V a n h o u t r y v e ' s b o o k The Statues of Bruges, p p . 22-23.

The p h o t o g r a p h w a s p r o v i d e d b y Mr . R. Jacobus , p r e s s a t tach6 for t he c i ty of Bruges .

Aarsthertogstraat 42 8400 Oostende Belgium

56 THE MATHEMATICAL INTELLIGENCER VOL. 18, NO. 3, 1996

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Collegium Logicum

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1996. Approx. 140 pages. ISBN 3-211-82796-X

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