SMURCHOM III
Schedule and Student Abstracts:
Registration & Refreshments
9:00-9:45 Stillwell Main Entrance
Welcome & Opening Remarks
9:50-10:00 Turner Auditorium, Natural Sciences Building
Keynote Speaker:
10:00-11:00 Turner Auditorium
Exploring the Best Joke of the 19th Century: The History of Mathematics in Action Dr. Deborah Kent, Simon Fraser University
Contributed Paper Session on the History of Mathematics
11:00-12:00 Turner Auditorium
11:00 Nicolas Bourbaki: Origins and Influence Amanda Collins and Constance Markley, Western Carolina University
11:20 A Closer Look into the Pythagorean Theorem: From Babylonia to China to Today’s Classroom Amy Adair, Jordan Davis, and Taryn Tyson, Western Carolina University
11:40 How to Find a Treasure-Trove of Resources on the History of Mathematics on the Web Sloan Despeaux, Western Carolina University
Lunch
12:00-2:00 WCU Picnic Shelter
Poster Presentations
2:00-2:45 455 Stillwell
See the Abstracts Sections for Poster Titles and Abstracts.
HOM on WEB Scavenger Hunt
2:45-3:30 148 and 149 Stillwell
Join in the Team Scavenger Hunt!! For all SMURCHOM Participants
Afternoon Refreshments
3:30-3:50 Turner Auditorium
Contributed Paper Session on Mathematics Informed by its History
3:50 - 4:50 Turner Auditorium
3:50 “ Mousetrap” from Cayley to Today Chris Johnson, Western Carolina University
4:30 Differentiation Shortcuts à la Descartes James Conrad Eubanks and M. Scott Wells University of North Carolina– Asheville
Closing Remarks
4:50 - 5:00 Turner Auditorium
Abstracts:
Keynote Address Exploring the Best Joke of the 19th Century: The History of Mathematics in Action
The story surrounding Neptune's discovery provides an exciting illustration of what historians of mathematics do. Neptune was first sighted as a new planet on 23 September 1846 at the Berlin observatory.
The sensational news reached London a week later and the ensuing dispute created one of the great (and ongoing) priority debates in the history of science. About a month after the initial observation, word of the new planet also arrived in America where the controversy captured both popular interest and scientific attention. A handful of nineteenth-century scientists who shared a vision for professionalizing science in America viewed the Neptune affair as an opportunity to establish the legitimacy of American science in response to perceived European scientific superiority. While European administrators of science quibbled over the priority question, the Harvard mathematician Benjamin Peirce---considered an upstart American scientist---dared to question the mathematical particulars of the discovery. Recent twentieth-century events and manuscript discoveries further illuminate the story of planetary controversy.
Amanda Collins and Constance Markley, Western Carolina University Nicolas Bourbaki: Origins and Influence
In 1934, the collective mathematician Nicolas Bourbaki was born at a café in Paris. His parents: five brilliant graduates of France’s distinguished l'École Normale Supérieure. These five mathematicians originally called themselves “The Committee for Writing a Treatise on Analysis” and had modest plans to replace the widely used Cours d'analyse mathématique (1902) by Edouard Goursat. Fueled by the depletion of French mathematicians and scientists following World War I, the group decided to mend mathematics in its entirety. The result is over seventy years of associated myth and mathematical works that emulate the axiomatic structure of Euclid’s Elements . The Bourbaki group has held tenaciously to their chosen mathematical philosophies: namely, the unity of all mathematics built upon set theory. Headed by André Weil and a handful of other founding members, Bourbaki first published in 1939. Over forty members and thousands of published pages later, the group is still publishing the proceedings of their successful non-specialized seminars held three times each year in Paris. Most concur that the group’s complete ambitions were never realized; however, the overall influence on the approach for which French mathematics is taught is generally acknowledged.
Amy Adair, Jordan Davis, and Taryn Tyson Western Carolina University A Closer Look into the Pythagorean Theorem: From Babylonia to China to Today’s Classroom
Throughout school most students learn about the Pythagorean Theorem’s Greek origins. In reality, the theorem was known well before the time of Pythagoras; additionally, it has been used an appreciated by a wealth of different cultures, including ancient Mesopotamia and China. This presentation discusses how these two cultures used this theorem and how we can incorporate this information into the elementary school classroom.
Sloan Despeaux, Western Carolina University How to Find a Treasure-Trove of Resources on the History of Mathematics on the Web
This talk will give a brief overview of the wealth of online sources for the history of mathematics. We will explore both primary and secondary sources available online. Hopefully, this talk will facilitate your own research in the history of mathematics. In the short term, it will aid you in the HOM on WEB Scavenger Hunt this afternoon.
Chris Johnson, Western Carolina University “ Mousetrap” from Cayley to Today
“Mousetrap” is a solitaire game devised by the English mathematician, Arthur Cayley, in which cards numbered one through n are placed a random permutation. The player then counts off cards, starting with the first card in the permutation, and removes the card from the permutation whenever the current card matches the player’s count. If all cards are removed in this manner, the player wins. If the player’s count reaches n without removing any cards, however, the player loses.
This talk concerns the development of Mousetrap from Cayley's original paper to more recent developments concerning the number of permutations satisfying various restrictions (e.g., the number of permutations where the cards are removed in order, in reverse order, etc.).
Sam Daoud, Western Carolina University Iso-Taxicab Geometry Retooled and Reworked
Taxicab geometry is a geometry in which two points are connected via a polygonal line made entirely from horizontal and vertical line segments, unlike Euclidean where a single straight line connects two points. In 1989, Katye Sowell formulated a new version of this geometry, which she called Iso-Taxicab geometry. In Iso-Taxicab geometry, two points are connected via a polygonal line made from three types of line segments: horizontal line segments, line segments that are angled 60 º from the positive x-axis, and line segments that are angled 120 º from the positive x-axis. Another way of thinking about it is that Taxicab geometry lies on a square lattice, whereas Iso-Taxicab geometry lies on a (equilateral) triangular lattice.
One of the main interests is to find the curvature of the space. The Iso-Taxicab space is not believed to be flat, but rather curved, like a spherical or hyperbolic space. The curvature is measured using a technique established by the twentieth-century Russian mathematician, Aleksandr Alexandrov.
James Conrad Eubanks and M. Scott Wells, University of North Carolina– Asheville Differentiation Shortcuts à la Descartes
In his Geometry , Descartes details an ingenious way of finding the tangent line to a point on an algebraic curve by finding the tangent circle. He is able to accomplish this feat algebraically by describing the intersection of the circle and the curve in terms of a parameter, and then finding the value of the parameter that yields a root of multiplicity two. In a letter shortly thereafter, he offers a simplification which utilizes a line, the curve and a different parameter, which may be recast by the modern reader as the slope of the line. Finding the value of the parameter that yields a “double root” is akin to computing the tangent slope. This second method affords an alternative way to derive the familiar differentiation shortcuts for rational polynomial functions which is both remarkable and completely algebraic. In this talk, the second method will be fully described and used to derive some of these familiar shortcuts.
Gina Billingsley and Sabrina Lane, Western Carolina University Mathematics in Iraq
The main objective of our poster is to illustrate what is occurring present-day with Iraq’s museums, libraries, and archeological sites. At the beginning of the war, the US and UK forces worked with Iraq to purposely avoided bombing any the museums, libraries, archeological sites, and any other sites where major manuscripts collections were known to be stored. Unfortunately, after the war started, there was little protection for these sites, and many sites have been looted and/or burned. Many items that remained or have been recovered are now being improperly stored and therefore being damaged further. To reverse the damage, some libraries and museums have begun the slow process of rebuilding. Donations are being made from various organizations and a few looters have returned the items they took during the looting.
Christa Conner and Polly Rudoff, Western Carolina University Cayley Connections
In our poster, we discuss Arthur Cayley’s work in mathematics and briefly cover his biographical information. We look at other concepts that are similar to his Cayley tables and make “connections.” For example, we summarize magic squares, sudoku squares, and Latin squares and explain how they are all similar to Cayley tables. We then discuss what Cayley tables are used for. Our poster is also interactive. There is a sudoku square and two magic squares that can be manipulated.
Jeff Foster, Western Carolina University Niels Henrick Abel
This poster concerns Abel and his contributions to mathematics. It will discuss his biography with special emphasis on his mathematical mentors, collaborators, and successors.
Leah G. Cope, Western Carolina University Euler and e
This poster discusses Leonhard Euler and his discovery of the natural base e . It gives a summary of Euler’s life and how it influenced his works in mathematics. It also discusses how Euler built upon his predecessors’ works and came upon the natural base e .
Melissa Halling, Western Carolina University and Southwestern Community College JN-25
When most people think of the Pacific battles in World War II, they first think of Pear Harbor. There are many other infamous battles and events that occurred in the Pacific theater, and one battle that receives its own share of attention is the Battle of Midway. A turning point, the Battle of Midway ended the Japanese navy's domination in the Pacific. One of the reasons for the Allied victory was the determined work of codebreakers in Hawaii, England, and Austrailia. These people worked tirelessly to break JN-25, the Japanese naval code. JN-25 was a collection of 5-digit numbers that stood for words, phrases, and letters. The code numbers were encrypted by adding a number mod 10 from a table of additives and then sent.
The codebreakers were slowly making progress. The difficulty was in the additives. Once they had a series of additives figured out, the codes themselves were not problem, because years earlier the Japanese code book had been secretly photographed. Then came a breakthrough. The breakthrough was the discovery of a flaw in the
code numbers. It was determined that the 5-digit numbers were multiples of 3. Knowing the flaw made finding the additives much easier, speeding up the process considerably, which allowed the codebreakers to get the information to commanders in the US Navy early enough for them to change their battle plans. Without the flaw, the codebreakers would not have been able to provide the needed information in time.
Meredith Hartzog, Western Carolina University Gauss
Johann Carl Friedrich Gauss was born on April 30, 1777, in Brunswick, Germany. He came from a humble background, but became one of the greatest mathematicians in history. He reportedly knew how to read and write before entering school, and before he was three years old he could count and perform elementary calculations. Before he was 19 he proved the constructability of the seventeen-sided regular polygon with only a straightedge and compass.
In 1791 he was introduced to a duke, who gave him a stipend to attend Collegiate Carolinum, and he stayed there from 1792 to 1795. Then he went to the University of Göttingen. He left in 1798 but returned for his Ph. D. in 1799, with an outstanding dissertation: he proved the Fundamental Theorem of Algebra. In 1801, Gauss calculated the orbit of the asteroid Ceres from only three appearances. In this work he introduced the bell curve, now called Gaussian Distribution. In 1805 he married Johanna Osthuff, but their marriage was short. In 1809, she died a month after childbirth. The baby followed a few months after; then Gauss became engaged to and married “Minna” Waldeck. After three childbirths, she died in 1831. In 1854, Gauss was diagnosed with dilation of the heart and died the next year.
Leia Hays, Western Carolina University Measuring the Universe
One thing that we look at as we explore history is what interests men in certain time periods and how that interest carries on or dies out. The history of mathematics is no exception. One thing that has never died is trying to determine the size of the great universe that we live in. Scholars have always built on the research of those before them as we do today. My poster will cover the first attempts at discovering the size of the universe, when the known universe consisted of the Earth, moon, sun, and the surrounding planets, up to the present day. It will also focus on great minds through the ages, such as, Aristarchus, Hipparchus, Copernicus, Edwin Hubble, and many more.
Truly Lucman, Western Carolina University Euler
This poster consists of an abridged version of Euler’s biography, his accomplishments in science, and Euler’s alternative solution to the quadratic solution. An application of this solution is also presented. Moreover, this poster discusses some trivia regarding the solution and Euler’s proposed fundamental theorem in algebra.
Hunter Thompson, Western Carolina University Cauchy
Augustin Loius Cauchy was an early nineteenth-century French mathematician who produced close to eight hundred mathematical works. Throughout his education, he heavily researched convergence and divergence of infinite series, differential equations, determinants, probability and mathematical physics. This poster focuses on his work pertaining to group theory.