Mathematics and Computer Programming
Published on 2010-02-06
Fractions produced by mediants have some very interesting properties. We saw some of them in connection with the Stern-Brocot tree. This articles explores a more curious property, relating fractions to circles in the plane. It was discovered in 1938 by Lester R. Ford and is also mentioned in Conway and Guy’s The Book of Numbers.
Published on 2010-01-09
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics is a book about the Riemann Hypothesis, posed by Bernhard Riemann in 1859. As the book title says, it is one of the greatest unsettled mathematical conjectures remaining today. It is among David Hilbert’s list of twenty-three mathematical problems and one of the seven millennium problems presented by the Clay Mathematics Institute.
Published on 2009-12-04
Consider two fractions \frac{m_1}{n_1} and \frac{m_2}{n_2} with positive numerators and denominators. The fraction \frac{m_1+m_2}{n_1+n_2} is called the mediant of \frac{m_1}{n_1} and \frac{m_2}{n_2}. It is straightforward to show that the mediant is placed numerically between the original fractions,
Published on 2009-11-15
The Pleasures of Counting is a book about people working with mathematics and challenges they have faced. The book has 544 pages with a total of 19 chapters and 3 appendices. It contains a lot of material and is split into five parts: The uses of abstraction, Meditations on measurement, The pleasures of computation, Enigma variations, and The pleasures of thought.
Published on 2009-11-10
We will be considering continued fractions of the form
Published on 2009-10-29
The greatest common divisor of two integers is the largest positive integer that divides them both. This article considers two algorithms for computing \hbox{gcd}(u,v), the greatest common divisor of u and v.
Published on 2009-09-23
The addition formulas for sine and cosine look like this:
I can never remember them.
Published on 2009-09-19
This is the first release of the SputArithmetic library. You can download the library or read about it.
Published on 2009-09-09
This articles explores some basic properties of the integer functions commonly known as floor and ceil. Most of the statements may seem trivial or obvious, but I, for one, have a tendency to forget just how exact you can be when it comes to expressions/equations where floor or ceil functions appear.
Useful Properties of the Floor and Ceil Functions continued »
Published on 2009-08-28
Let us revisit the geometric progression sum considered in an earlier article,
where r here is a complex number. For what values of r does this infinite sum make sense? Can we find a closed-form expression for s_r in such cases? To investigate this, we fix r to some value and consider the partial sums:
On the Divergence of a Geometric Progression Sum continued »
