Displaying similar documents to “Decorations by Means of Generalized Clothoids”

Caustics in Greek antiquity

Alain Joets (2008)

Banach Center Publications

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The word caustic was introduced by Tschirnhausen in 1686, in the Latin expression caustica curva. We show that the study of the optical caustics goes back well before, at least to the hellenistic period. We present a small Greek text, whose author is perhaps Geminus (1st cent. B.C.), describing an optical phenomenon called achilles. We show that the term achilles, which has appeared only once, to our knowledge, in the literature, means caustics by reflection. We complete the description...

On Christoffel classes

Jean-Pierre Borel, Christophe Reutenauer (2006)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We characterize conjugation classes of Christoffel words (equivalently of standard words) by the number of factors. We give several geometric proofs of classical results on these words and sturmian words.

Geometrical Patterns in the Pre-classical Greek Area. Prospecting the Borderland between Decoration, Art, and Structural Inquiry

Jens Høyrup (2000)

Revue d'histoire des mathématiques

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Many general histories of mathematics mention prehistoric “geometric” decorations along with counting and tally-sticks as the earliest beginnings of mathematics, insinuating thus (without making it too explicit) that a direct line of development links such decorations to mathematical geometry. The article confronts this persuasion with a particular historical case: the changing character of geometrical decorations in the later Greek area from the Middle Neolithic through the first millennium...

Directive words of episturmian words: equivalences and normalization

Amy Glen, Florence Levé, Gwénaël Richomme (2008)

RAIRO - Theoretical Informatics and Applications

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Episturmian morphisms constitute a powerful tool to study episturmian words. Indeed, any episturmian word can be infinitely decomposed over the set of pure episturmian morphisms. Thus, an episturmian word can be defined by one of its morphic decompositions or, equivalently, by a certain directive word. Here we characterize pairs of words directing the same episturmian word. We also propose a way to uniquely define any episturmian word through a normalization of its directive words....

The Area and the Side I Added: Some old Babylonian Geometry

Duncan J. Melville (2005)

Revue d'histoire des mathématiques

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There was a standard procedure in Mesopotamia for solving quadratic problems involving lengths and areas of squares. In this paper, we show, by means of an example from Susa, how area constants were used to reduce problems involving other geometrical figures to the standard form.