## Stifel and Roberval

Michael Stifel was a German mathematician who lived in the late fifteenth century and early to mid-sixteenth century. He was born in 1487 in Esslingen, Germany.

The exact date of his birth is unknown. Stifel died on April 19, 1567, in Jena, Germany. His father was Conrad Stifel, a well-respected member of the community. When Michael was young, his family did not have much money. Not much is known about Stifel’s life until the time he attended the University of Wittenberg in Germany. After he graduated, Stifel was awarded an M.A. from the university. Then Stifel began his life with the church. He entered the Augustinian monastery and became a Catholic priest in 1511. Soon after this, Stifel began questioning the Catholic Church. He did not like the idea of taking money from poor people.

As a result of this, Stifel was forced to leave the monastery in 1522. Now he decided to go to Wittenberg and become a Lutheran. During this time, Stifel became friends with Martin Luther himself and lived in his house for a time. In 1523, Martin Luther made Stifel a pastor, but because of anti-Lutheran feelings, Stifel was forced to leave this job. Then in 1528, Martin Luther decided to give Stifel a parish in Lochau, which is now Annaberg.

This is where Stifel’s story gets wacky. While in Lochau, Stifel decided to announce to everyone that the world was going to end on October 19, 1533, at exactly 8:00 AM. It seems that Stifel performed a series of calculations in which he changed the letters to their successive triangular numbers. However, how these calculations proved that the world was coming to an end is beyond my comprehension of mathematics.

Stifel told the people of Lochau of his “findings” on New Year’s Eve of 1522. This announcement had amazing repercussions. The sleepy town of Lochau believed Stifel. They all began living for the day and not worrying about what the future would bring. They did not bother to plant crops or store what food they had.

Lochau also became a destination for pilgrims. Once they got to Lochau, people began to prepare for the end of the world. Some people even took their own lives instead of waiting. Some of the town’s people burned their houses in an attempt to remove themselves from material objects and make it easier to get to “Heaven.” Lochau had only two bars, and in the time between Stifel’s announcement and “the end,” it was said that they were never empty. The owners gave away free drinks.

The owners of the town’s inns also let people stay there for free. While all of this was happening, Lochau’s historian took all the money from the treasury and left. As a result of this craziness, Stifel was forbidden to preach. Finally, the “last day” came and Stifel began to prepare his followers for the end.

Fortunately for everyone except Stifel, the world did not end that day. At 8:30 AM, the authorities took Stifel away and put him in protective custody for his own protection. Crowds gathered outside his cell and chanted “Stifel must die” for many days after this. Martin Luther got Stifel out of this, but he had to promise not to make any more prophecies. Another one of Stifel’s adventures had to do with the newly crowned pope, Leo X.

Since he was a Lutheran, Stifel was not too fond of Leo, and he had the calculations to back up his opinions. Stifel took the name Leo X and wrote it in Latin; this was LEO DECIMVS. He then assigned the numerical counterparts (Roman numerals) of these letters, throwing out the non-numerical E, O, and S. He arranged the remaining letters and came up with MDCLVI.

The next “logical” step was to add back the X from Leo’s original name, and Stifel had MDCLXVI. He then took off the M because it was the initial of mysterium, a word for a religious mystery. The result was DCLXVI, or six hundred sixty-six, or 666. According to Stifel, this proved that Pope Leo X was indeed the Antichrist.

In response to this, Peter Bungus, a Catholic theologian, decided to write a 700-page book to prove that it was not Leo X but Martin Luther who was the Antichrist. Aside from these most interesting situations, Stifel did make some real contributions to mathematics. His most famous work is the book Arithmetica Integra. In this book, one of the earliest logarithm tables can be found, which is very similar to the ones we use today.

Stifel invented logarithms using a method unique to the one that Napier used. Probably the most important contribution Stifel made was that he was the first European mathematician to use the addition, subtraction, and square root symbols: +, -, and √. Stifel also made other contributions to algebra and basic arithmetic. Michael Stifel was, in the kindest terms, an eccentric mathematician.

His work has helped the development of algebra, and he helped to shape modern mathematics. However, his ideas on the end of the world and about Leo X most likely overshadow the good he has done. A page from Arithmetica Integra is shown below. Another page from Arithmetica Integra is shown below.

Roberval Gilles Personne Roberval was born in Senlis, France, on August 10, 1602. He was a French mathematician who died on October 27, 1675, in Paris. He came from a family of simple farmers with a simple way of life.

Since his family was poor, Roberval had no official schooling. His family taught him until he left home sometime before his fourteenth birthday. At the age of fourteen, Roberval’s interest in mathematics was born. Roberval traveled all over France earning money by giving private lessons. He also talked with many professors at universities about many advanced topics.

Once while Roberval was in Bordeaux, he met Fermat. Because of this meeting, Roberval was selected to participate in the group that met with Mersenne. Roberval arrived in Paris in 1628, where he met with the group. He took a particular interest in Mydorge, Etienne Pascal, and Blaise Pascal.

It is interesting to note that even with the talent that was present in this group, Roberval was the only one who went on to become a professional mathematician. In 1632, Roberval was made professor of philosophy at the College Gervais in Paris. Then in 1634, he was given the Ramus chair of mathematics in the College Royale. This basically meant he was in charge of the math department at the college. One of Roberval’s greatest accomplishments was being elected to the Academie Royal des Sciences in 1666. He was one of the founding members of the Academie.

During his life, Roberval worked on many topics. He was a supporter of the geometry of infinitesimals, which he said was created by Archimedes. Roberval was unaware of the work that Cavalieri had done. Roberval wrote a book about finding areas called Traite des Indivisibles. The Academie published this with a collection of works.

Roberval wrote treatises on algebra and analytic geometry. He is known as the father of kinematic geometry because of his work with the “composition of movements”. This is most useful in finding tangents. Probably the most famous invention of Roberval’s would be the Roberval balance, which is used almost everywhere today. He also helped Italy with the barometric experiments and worked with Pascal on the vacuum apparatus and experiments.

Unfortunately, during his life, Roberval did not achieve much notoriety because his work took place at the same time as Fermat and Pascal. Roberval also worked on curves. Among his most famous are: the Cycloid, the Limacon of Pascal, the Cissoid of Diocles, and the Folium of Descartes.

Cycloid: The cycloid is the locus of a point at distance h from the center of a circle radius a that rolls along a straight line. If h * a, it is a curtate cycloid while if h * a, it is a prolate cycloid. This curve has a = h.

Limacon of Pascal: This curve was discovered by Etienne Pascal, the father of Blaise Pascal. However, it was named by Roberval in 1650 when he used it as an example of his methods of drawing tangents. The name Limacon comes from the Latin word limax which means a snail. While Roberval is often given credit for this curve, many of the members of the Mersenne group contributed to its development. When b = 2a, then the limacon becomes a * a while if b = a, then it becomes a trisectrix.

### Cissoid of Diocles: (No information)

Folium of Descartes: This curve was first thought of in 1638, but Roberval believed that the leaf shape was repeated in each quadrant when it is only in quadrant I. This curve has an asymptote x + y + a = 0. This curve passes through the origin at t = 0 and comes close to the origin as t goes to infinity.