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#### On two types of exotic addition

(Aequationes Mathematicae, 2009)

We classify, under reasonable assumptions, all differentiable functions f for which the 'secant method' [xf(y)- yf(x)]/[f(y)- f(x)] is continuous and associative. Further, we classify all differentiable functions for which ...

#### On integral Apollonian circle packings

(Journal of Number Theory, 2006)

The curvatures of four mutually tangent circles with disjoint interior form what is called a Descartes quadruple. The four smallest curvatures of circles in an Apollonian circle packing form what is called a root Descartes ...

#### Associativity of the Secant Method

(American Mathematical Monthly, 2002)

Iterating a function like 1+1/x gives a sequence which converges to the Golden Mean but does so at a much slower rate than those sequences derived from Newton's method or the secant method. There is, however, a surprising ...

#### Not mixing is just as cool

(Mathematics Magazine, 2007)

Newton's law of cooling, a staple of the Calculus curriculum, is an empirical law not meant for mathematical proof. However, we show it is mathematically equivalent to the intuitively appealing principle that the average ...