Category Archives: Vignette
How to get rid of quantifiers?
Originating authors are Reinhard Oldenburg and Michele Artigue. How do computer packages do abstract algebraic problems such as proving statements “for all ” or finding whether a Real Number with certain conditions exists? Recent advances draw on theorems in mathematical … Continue reading
The Revenge of the Infinitesimals
Originating author is Michèle Artigue. Infinitesimals played an essential role in the emergence and development of differential and integral calculus. The evident productivity of this calculus did not prevent recurrent and fierce debates about the nature of these objects and … Continue reading
Classifying objects
Originating author is Christiane Rousseau. Mathematics offers tools for classifying objects. But is that of any practical use? More than we can imagine at first sight… It could allow us to conclude that a knot cannot be unknotted without cutting … Continue reading
The Hairy Ball Theorem
Originating author is João Pimentel Nunes The Hairy Ball Theorem is from topology, that part of mathematics that is concerned with the form of spaces. For the most part, this result came from work at the end of the 19th … Continue reading
Calculators, Power Series and Chebyshev Polynomials
Originating author is Graeme Cohen. Of all the familiar functions, such as trigonometric, exponential and logarithmic functions, surely the simplest to evaluate are polynomial functions. The purposes of this article are, first, to introduce the concept of a power series, … Continue reading
Dimension
Von Christiane Rousseau Übersetzt aus dem Englischen von Eva Klein (Universität Würzburg) Wie misst man die Größe eines geometrischen Objekts? Für Teilmengen einer Ebene verwenden wir dazu oft Umfang, Länge, Flächeninhalt, Durchmesser, etc. Diese Maßbegriffe reichen jedoch nicht aus, um … Continue reading
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The shocking behaviour of moving fluids
Originating authors are David Mumford and Christiane Rousseau. Foreword: This vignette is more difficult than others. However, in a few pages, it tells you how to explain in simple terms one of the most difficult open problems at the beginning … Continue reading
Public-key cryptography
Originating authors are Graeme L. Cohen (University of Technology, Sydney), Steven Galbraith (University of Auckland) and Edoardo Persichetti (University of Auckland). How can we safely send our credit card details over the internet, or using a mobile phone, when others … 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
SXEOLF NHB FUBSWRJUDSKB (PUBLIC KEY CRYPTOGRAPHY)
The need to create secure codes is said to go back to Julius Caesar, who moved letters in his messages up by three through the alphabet. That is encoding. How would you decode such a message? Modern day cryptography, which … Continue reading
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