FREE ESSAY ON STIFEL AND ROBERVAL

STIFEL AND ROBERVAL

Michael Stifel
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.