Building Moebius Bands

We are all familiar with the Möbius strip or Möbius band. This topologically intriguing object with one side and one edge has fascinated children of all ages since it was discovered independently by August Möbius and Johann Listing in the same year, 1858. Building the Band It is a simple matter to make a Möbius … Continue reading Building Moebius Bands →

Andrey Markov’s Brilliant Ideas are still a Driving Force

Imagine examining the first 20,000 letters of a book, counting frequencies and studying patterns. This is precisely what Andrey Markov did when he analyzed the text of Alexander Pushkin's verse novel Eugene Onegin. This work comprises almost 400 stanzas of iambic tetrameter and is a classic of Russian literature. Markov studied the way vowels and … Continue reading Andrey Markov’s Brilliant Ideas are still a Driving Force →

Moessner’s Magical Method

Amongst the many joys of mathematics are the beautiful patterns that appear unexpectedly from time to time. In 1951, Alfred Moessner discovered a delightful and ingenious way of generating sequences of powers of natural numbers. It is surprisingly simple and offers great opportunities for development and generalization. It is well-known that the sum of odd … Continue reading Moessner’s Magical Method →

Euler and the Fountains of Sanssouci

When Frederick the Great was crowned King of Prussia in 1740 he immediately revived the Berlin Academy of Sciences and invited scholars from throughout Europe to Berlin. The most luminous of these was Leonhard Euler, who arrived at the academy in 1741. Euler was an outstanding genius, brilliant in both mathematics and physics. Yet, a … Continue reading Euler and the Fountains of Sanssouci →