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## Book of the Month: Developing Research in Mathematics Education

August’s book of the month is Developing Research in Mathematics Education: Twenty Years of Communication, Cooperation and Collaboration in Europe, edited by Tommy Dreyfus, Michèle Artigue, Despina Potari, Susanne Prediger, and Kenneth Ruthven. It is the first book in the … Continue reading

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## How Google works: Markov chains and eigenvalues

Originating author is Christiane Rousseau. From its very beginning, Google became “the” search engine. This comes from the supremacy of its ranking algorithm: the PageRank algorithm. Indeed, with the enormous quantity of pages on the World-Wide-Web, many searches end up … Continue reading

## Dimension

Originating author is Christiane Rousseau. How do we measure the size of a geometric object? For subsets of the plane we often use perimeter, length, area, diameter, etc. These are not sufficient to describe fractals. The fractal objects are very … Continue reading

## Fair voting: the quest for gold

Originating authors are Gabriel Rosenberg and Mark Iwen. It is a little known fact that two gold medals were awarded for the same pairs figure skating competition in the 2002 Winter Olympics. These two medals were ultimately a result of … Continue reading

## Banach’s microscope to find a fixed point

Originating author is Christiane Rousseau. In this vignette, we will show how we start from a small game to discover one of the most powerful theorems of mathematics, namely the Banach fixed point theorem. This theorem has fantastic applications inside … Continue reading

## A tale of two triangles: Heron triangles and elliptic curves

Originating author is William Mc Callum. If two triangles have the same area and the same perimeter, are they necessarily congruent? It turns out that the answer is no. For example, the triangle with sides and has the same area … Continue reading