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#### The Brachistochrone Problem: Mathematics for a Broad Audience via a Large Context Problem

(Montana Council of Teachers of Mathematics & Information Age Publishing, 2008)

Large context problems (LCP) are useful in teaching the history of science. In this article we consider the brachistochrone problem in a context stretching from Euclid through the Bernoullis. We highlight a variety of ...

#### Attainable lengths for circular binary words avoiding k-powers

(The Belgian Mathematical Society, 2005)

We show that binary circular words of length n avoiding 7/3+ powers exist
for every sufficiently large n. This is not the case for binary circular words
avoiding k+ powers with k < 7/3

#### Avoiding Patterns in the Abelian Sense

(Canadian Mathematical Society, 2001-08)

We classify all 3 letter patterns that are avoidable in the abelian sense. A short list of four letter patterns for which abelian avoidance is undecided is given. Using a generalization of Zimin words we deduce some ...

#### Sliding Down Inclines with Fixed Descent Time: a Converse to Galileo's Law of Chords

(Canadian Mathematical Society, 2008-12)

#### Least Periods of Factors of Infinite Words

(EDP Sciences, 2009)

We show that any positive integer is the least period of a factor of the Thue-Morse word. We also characterize the set of least periods of factors of a Sturmian word. In particular, the corresponding set for the Fibonacci ...

#### Non-Repetitive Tilings

(The Electronic Journal of Combinatorics, 2002-07-03)

In 1906 Axel Thue showed how to construct an infinite non-repetitive (or square-free) word on an alphabet of size 3. Since then this result has been rediscovered many times and extended in many ways. We present a two-dimensional ...

#### Regular Two-Graphs and Equiangular Lines

(University of Winnipeg, 2004)

Regular two-graphs are antipodal distance-regular double coverings of the complete graph, and they have many interesting combinatorial properties. We derive a construction for regular two-graphs containing cliques of ...

#### Mathematical Concepts and Proofs from Nicole Oresme: Using the History of Calculus to Teach Mathematics

(2005)

This paper examines the mathematical work of the French bishop, Nicole Oresme (c. 1323–1382), and his contributions towards the development of the concept of graphing functions and approaches to investigating infinite ...

#### Dejean's conjecture holds for n ≥ 27

(EDP Sciences, 2009)

We show that Dejean’s conjecture holds for n ≥ 27. This brings the final resolution of the conjecture by the approach of Moulin Ollagnier within range of the computationally feasible.

#### There Exist Binary Circular 5/2+ Power Free Words of Every Length

(The Electronic Journal of Combinatorics, 2004-01-23)

We show that there exist binary circular 5/2+ power free words of every length.