## Uniqueness of hyperbolic geodesics

The Poincare’ model of hyperbolic geometry consists of the unit disk where the geodesics are arcs of circles perpendicular to the unit circle . It turns out that given two points there is a unique circle orthogonal to passing through … Continue reading

## Modulus of Path Families on Graphs

These notes approximately follow a presentation Mario Bonk gave at the Workshop on Discrete and Complex Analysis, Montana State University, July 19-23, 2010. We follow the paper of Haïssinsky “Empilements de cercles et modules combinatoires”. Ann. Inst. Fourier (Grenoble) 59 … Continue reading

## An elementary introduction to data and statistics

The first part of this material should be accessible to a fourth-grader, the latter part to a middle-schooler. The initial Mental Math trick can be taught without algebra, even though in order to describe the method on paper we found … Continue reading

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## On the Euclidean Growth of Entire Functions

In Mapping properties of analytic functions on the unit disk, Proceedings of the American Mathematical Society, Vol. 135, N. 9 (2007), 2893-2898. I show that there is a universal constant such that whenever is analytic in the unit disk and … Continue reading

## Square-roots of Complex Numbers

If is a complex number in polar coordinates, with say , then one of its square-roots is . But what if one wants to avoid using the exponential function? This trick was related to me by my colleague Bob Burckel. … Continue reading

## Complex Numbers

A complex number can be written in Cartesian coordinates as , where is the real part and is the imaginary part. Or it can be written in polar coordinates as , where is the absolute value and is the point … Continue reading

## An Elementary Introduction to Data and Statistics

Elementary Introduction to Data and Statistics

## Limit hulls?

In the course of trying to explain and “visually” I was led to this variation on the notion of convex hull. Given a set in the plane, the convex hull is constructed by considering all the half-planes that contain and … Continue reading