Open Access. Powered by Scholars. Published by Universities.®
University of Nebraska - Lincoln
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
Articles 1 - 9 of 9
Full-Text Articles in Education
Wythoff’S Game, Kimberly Hirschfeld-Cotton
Wythoff’S Game, Kimberly Hirschfeld-Cotton
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
Wythoff’s Game, named after Willem Abraham Wythoff, is a well known game amongst number theorists. Dr. Wythoff, who received a Ph. D. in mathematics from the University of Amsterdam in 1898, described this game in these words: “The game is played by two persons. Two piles of counters are placed on a table, the number of each pile being arbitrary. The players play alternately and either take from one of the piles an arbitrary number of counters or from both piles an equal number. The player who takes up the last counter or counters, wins.” This game was previously known …
The Game Of Bridg-It, Sandy Dean
The Game Of Bridg-It, Sandy Dean
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
On the surface, Bridg-It appears to be a simple game of connecting dots to form lines across the board. Playing Bridg-It is simple. Understanding and playing Bridg-It well is more complicated. To understand the theory and strategy behind Bridg-It, one must first understand certain elements of graph theory, such as disjoint spanning trees. Only then can one master the game of Bridg-It.
The Polar Coordinate System, Alisa Favinger
The Polar Coordinate System, Alisa Favinger
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
Representing a position in a two-dimensional plane can be done several ways. It is taught early in Algebra how to represent a point in the Cartesian (or rectangular) plane. In this plane a point is represented by the coordinates (x, y), where x tells the horizontal distance from the origin and y the vertical distance. The polar coordinate system is an alternative to this rectangular system. In this system, instead of a point being represented by (x, y) coordinates, a point is represented by (r, θ) where r represents the length of a straight line from the point to the …
De Bruijn Cycles, Val Adams
De Bruijn Cycles, Val Adams
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
Problem 1. A robot is moving on a cyclic track. The track is marked at evenly spaced intervals with 0s and 1s, with a total of 8 marks. The robot can see the 3 marks closest to him. How should the 0s and 1s be put on the track so that the robot knows where on the track he is by just looking at the 3 closest marks?
Problem 2. The city of Konigsberg, Prussia is set on the Pregel River and includes two large islands, which are connected to each other and the mainland by seven bridges. Is it …
Archimedean Solids, Anna Anderson
Archimedean Solids, Anna Anderson
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
A polygon is a simple, closed, planar figure with sides formed by joining line segments, where each line segment intersects exactly two others. If all of the sides have the same length and all of the angles are congruent, the polygon is called regular. The sum of the angles of a regular polygon with n sides, where n is 3 or more, is 180° x (n – 2) degrees. If a regular polygon were connected with other regular polygons in three dimensional space, a polyhedron could be created. In geometry, a polyhedron is a threedimensional solid which consists of a …
Mathematics And Evolution, Kacy Heiser
Mathematics And Evolution, Kacy Heiser
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
What is game theory and how does it apply to Evolutionary Biology? Game theory was originally developed to help portray how individuals interact with each other and it was mainly used in the economics and political science fields. This area of mathematical study came about after World War II and was developed by John von Neumann and Oskar Morgenstern. It wasn’t until the 1970’s that George Price and John Maynard Smith began to apply game theory to evolution in trying to predict the behavior of animals in a species. There are two main evolutionary trends we will study using game …
Lester’S Circle, Julie Hoaglund
Lester’S Circle, Julie Hoaglund
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
Euclid is credited with most of the theorems in geometry textbooks today. Around 300 B.C., Euclid produced a thirteen volume publication called The Elements. These volumes include much information others had studied. Throughout history, many great mathematicians including Pasch, Hilbert, and Birkhoff have studied and tried to improve Euclidean geometry. Groups such as University of Chicago School Mathematics Project have made improvements on the Euclid’s axiomatic system.
The Kaprekar Routine, Emy Jones
The Kaprekar Routine, Emy Jones
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
There is a story about a man named “Joe” whose wife sent him to the supermarket. Joe was never a very good listener – he tended to pick up on the major points of a conversation, but never seemed to get things in the right order. So when he arrived at the store, he headed straight for the garlic section (for he was sure that his wife had mentioned garlic). However, when he got there, he stared at the $10 bill in his hand. She had asked him to buy $4.95 worth of garlic, or was it $9.54, or maybe …
The Square Root Of I, Tiffany Lothrop
The Square Root Of I, Tiffany Lothrop
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
While Girolamo Cardano was working on solving cubic and quadratic equations in 1539, he encountered some formulas that involved square roots of negative numbers. In 1545 Cardano published Ars Magna, where he presents the first recorded calculations that involve complex numbers. Then in 1572, Rafael Bombelli published the first three parts of his Algebra. He is known as the inventor of complex numbers, because he identifies some rules for working with them. Bombelli also shows how complex numbers are very important and useful. From Bombelli’s list of rules for adding, subtracting and multiplying the complex numbers, he was able to …