Essay, Research Paper: Stifel And Roberval


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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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