# Essay, Research Paper: Stifel And Roberval

## Mathematics

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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 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 Wittnenberg 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 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 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 life 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 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 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 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 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

rearranged 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 is one of earliest logarithm tables,

which is very similar to the ones we use today. Stifel invented logarithms using

a method unique to the method that Napier used. Probably the most important

contribution Stifel made was in 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 as 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 ntegra Another page from Arithmetica Integra

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 head 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. As is clearly evident

through this information, both Michael Stifel and Gilles Personne de Roberval

made great contributions to the world of mathematics. Life today would just not

be the same if these two men had not done their important work.

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