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...

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...

We will be considering continued fractions of the form a_0 + \displaystyle\frac{1}{a_1 + \displaystyle\frac{1}{\ddots + \displaystyle\frac{1}{a_{n-1} + \displaystyle\frac{1}{a_n}}}} where the a_k’s are real numbers called the partial quotients....

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. Some key properties of \hbox{gcd}...

The addition formulas for sine and cosine look like this: \begin{aligned} \cos(\alpha + \beta) &= \cos \alpha \cos \beta – \sin \alpha \sin \beta, \\ \sin(\alpha + \beta) &= \sin \alpha \cos \beta + \cos \alpha \sin \beta. \\ \end{aligned} I can...