Author Archives: Antoine Nectoux

Goodstein Sequences: The Power of a Detour via Infinity

Originating authors are Michèle Artigue, Ferdinando Arzarello and Susanna Epp. Studying the evolution of a natural phenomenon often leads to studying numerical sequences , especially their long-term behavior and whether they eventually converge. Polynomial, exponential, and logarithmic sequences are frequently … Continue reading

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Matrices and Digital Images

Originating authors are Dirce Uesu Pesco and Humberto José Bortolossi. The images you see on internet pages and the photos you take with your mobile phone are examples of digital images. It is possible to represent this kind of image … Continue reading

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What is the way of packing oranges? — Kepler’s conjecture on the packing of spheres

Originating author is Christiane Rousseau. What is the densest packing of spheres? Kepler conjectured that it was the one you observe with oranges at the fruit shop, and which is called the face-centered cubic lattice (Figure 1). At the International … Continue reading

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Higher Dimensions

Originating authors are Markus Ruppert and Hans-Georg Weigand. 1. Looking for the next dimension Does our world really have more than three dimensions? If so, do objects in higher dimension have a relation to the world around us? Is it … Continue reading

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Benford’s law: learning to fraud or to detect frauds?

Originating author is Christiane Rousseau. It is very risky to change too many numbers in some fi nancial statements if one does not know some mathematics. Indeed, most often the numbers appearing in fi nancial statements follow some strange mathematical rule, called … Continue reading

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Map colouring and Gröbner Bases

Originating author is Marcelo Escudeiro Hernandes. By the famous “Four Colour Theorem”, only four colours we need to colour a map so that no bordering regions have the same colour. Using polynomial equations and Gröbner bases we can determine if … Continue reading

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Symmetry Step by Step

Originating author is Ana Cannas da Silva. Symmetry has always fascinated and served humankind in architecture, arts, engineering and science. Over thousands of years symmetric patterns have been used to create fabrics, baskets, floors, wallpapers and wrapping papers, and so … Continue reading

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Recurrence and induction

Originating authors are Michèle Artigue and Ferdinando Arzarello. Given a square grid, it is easy to draw squares whose vertices are intersections of the grid lines. But is it possible to do so for other regular polygons, for instance an … Continue reading

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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

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Elementary Mathematics from an Advanced Standpoint

From now on we will feature a different book every month that is likely to be of interest to secondary teachers wanting to know more about mathematics. We have made the decision to use this feature to bring older books … Continue reading

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