Stifel And RobervalMichael Stifel was a German mathematician who lived in the late fifteenthcentury 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 thecommunity. When Michael was young his family did not have much money. Not muchis known about Stifel’s life until the time he attended the University ofWittenberg, in Germany. After he graduated, Stifel was awarded an M.

A. from theuniversity. Then Stifel began his life with the church. He entered theAugustinian monastery and became a catholic priest in 1511. Soon after this,Stifel began questioning the Catholic Church. He did like the idea of takingmoney from poor people.

Order nowAs a result of this, Stifel was forced to leave themonastery in 1522. Now he decided to go to Wittnenberg and become a Lutheran. During this time, Stifel became friends with Martin Luther himself, and lived inhis house for a time. In 1523, Martin Luther made Stifel a pastor, but becauseof 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 where Stifel’s story gets wacky. While in Lochau, Stifel decided toannounce to everyone that the world was going to end on October 19, 1533 atexactly 8:00 AM. It seems that Stifel performed a series of calculations inwhich he changed the letters to their successive triangular numbers. However,how these calculations proved that the world was coming to end is beyond mycomprehension of mathematics.

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

Lochau also became adestination for pilgrims. Once they got to Lochau people began to prepare forthe end of the world. Some people even took their own life instead of waiting. Some of the town’s people burned their houses in an attempt to remove themselvesfrom material objects and make it easier for 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 owner’s gaveaway free drinks.

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

Fortunately for everyone except Stifel the world didnot end that day. At 8:30 AM the authorities took Stifel away and put him inprotective custody, for his own protection. Crowds gathered outside his cell andchanted “Stifel must die” for many days after this. Martin Luther gotStifel out of this, but he had to promise not to make anymore 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 thecalculations to back up his opinions. Stifel took the name Leo X and wrote it inLatin; this was LEO DECIMVS. He then assigned the numerical counterparts (RomanNumerals) of these letters, throwing out the non-numerical E, O, and S. Herearranged the remaining letters and came up with MDCLVI.

The next”logical” step was to add back the X from Leo’s original name andStifel had MDCLXVI. He then took off the M because it was the initial ofmysterium, a word for a religious mystery. The result was DCLXVI, or six hundredsixty-six, or 666. According to Stifel this proved that Pope Leo X was indeedthe 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 MartinLuther who was the Antichrist. Aside from these most interesting situations,Stifel did make some real contributions to mathematics. His most famous work isthe book Arithmetica Integra. In this book is one of earliest logarithm tables,which is very similar to the ones we use today.

Stifel invented logarithms usinga method unique to the method that Napier used. Probably the most importantcontribution Stifel made was in that he was the first European mathematician touse the addition, subtraction, and square root symbols: +, -, and . Stifel alsomade other contributions to algebra and basic arithmetic. Michael Stifel was, inthe kindest terms, an eccentric mathematician.

His work as helped thedevelopment of algebra, and he helped to shape modern mathematics. However hisideas on the end of the world and about Leo X most likely overshadow the good hehas done. A page from Arithmetica ntegra Another page from Arithmetica IntegraRoberval 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. Hecame from a family of simple farmers with a simple way of life.

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

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

It is interesting to note that even with the talent that waspresent in this group, Roberval was the only one who went on to become aprofessional mathematician. In 1632, Roberval was made professor of philosophyat the College Gervais in Paris. Then in 1634, he was given the Ramus chair ofmathematics in the College Royale. This basically meant he was in head of themath department at the college. One of Roberval’s greatest accomplishments wasbeing elected to the Academie Royal des Sciences in 1666.

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

Roberval wrote treatises onalgebra and analytic geometry. He is known as the father of kinematic geometrybecause of his work with the “composition of movements”. This is mostuseful in finding tangents. Probably the most famous invention of Roberval’swould be the Roberval balance, which is used almost everywhere today. He alsohelped Italy with the barometric experiments, and worked with Pascal on thevacuum apparatus and experiments.

Unfortunately, during his life Roberval didnot achieve much notoriety because his work took place at the same time asFermat 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 ofDescartes. Cycloid: The cycloid is the locus of a point at distance h from thecenter of a circle radius a that rolls along a straight line. If h * a it is acurtate 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 ofBlaise Pascal. However, it was named by Roberval in 1650 when he used it as anexample of his methods of drawing tangents. The name Limacon comes from theLatin word limax which means a snail. While Roberval is often given credit forthis curve, many of the members of the Mersenne group contributed to itsdevelopment.

When b = 2a then the limacon becomes a * a while if b = a then itbecomes a trisectrix. Cissoid of Diocles: (no information) Folium of Descartes:This curve was first thought of in 1638, but Roberval believed that the leafshape was repeated in each quadrant when it is only in quadrant I. This curvehas an asymptote x + y + a = 0. This curve passes through the origin at t = 0and comes close to the origin as t goes to infinity. As is clearly evidentthrough this information, both Michael Stifel and Gilles Personne de Robervalmade great contributions to the world of mathematics. Life today would just notbe the same if these two men had not done their important work.