Displaying similar documents to “A geometrical description of visual sensation II”

Universal natural shapes

Johan Gielis, Stefan Haesen, Leopold Verstraelen (2005)

Kragujevac Journal of Mathematics

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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...

The PDE describing constant mean curvature surfaces

Hongyou Wu (2001)

Mathematica Bohemica

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We give an expository account of a Weierstrass type representation of the non-zero constant mean curvature surfaces in space and discuss the meaning of the representation from the point of view of partial differential equations.

Invariants and Bonnet-type theorem for surfaces in ℝ4

Georgi Ganchev, Velichka Milousheva (2010)

Open Mathematics

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In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map ofWeingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type for this frame field, we obtain eight invariant functions. We prove a fundamental theorem of Bonnet-type, stating that these eight invariants under some natural conditions determine the surface up to a motion. We show that the basic geometric classes...