Jean Constant - Solitons
Submitted by Jean Constant on
Variation on pseudo spherical surfaces (Soliton and Breather) created for an IRCAM - Mathematics and Music symposium in Paris, 2010.
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Jean Constant - Sangaku
Submitted by Jean Constant on
Sangaku were colorful tablets found in Shinto shrines in Japan during the Edo period and posing mathematical problems. They related to both principle of Euclidean geometry and more advanced mathematical issues requiring calculus and affine transformations. They were also original examples of widespread use of visualization in the teaching and appreciation of mathematics.
Jean Constant - Polyhedra
Submitted by Jean Constant on
Polyhedra refer to a variety of related constructs, some geometric, others purely algebraic or abstract. Often named after the number of faces they have, most polyhedra are symmetrical and provides a geometric perspective for problems in linear programming. The following is an attempt at blending pure programming visualization and geometry.
Jean Constant - Pattern recognition
Submitted by Jean Constant on
Pattern recognition deal with issues in cognitive and neuroscience as well as mathematics, particularly in CAD systems, optical recognition and image analysis. From abstract outline classification to the addition of shapes, forms and color scheme and visualization techniques it allows a better understanding of the complexity of mapping and recognition in the visual environment.
Jean Constant - Sphere eversion
Submitted by Jean Constant on
From the work of mathematician Richard Denner on polyhedral eversions. Two-dimensional interpretation of a three dimensional problem.
Jean Constant - Hyperbolas
Submitted by Jean Constant on
Two example from a 23 illustration series based on a template by software design engineer Bernie Freidin and available at http://www. hermay.org/jconstant/hyperboles/
Jean Constant - Knots
Submitted by Jean Constant on
Two examples of a 23 knot portfolio available at http://www. hermay.org/jconstant/dknots/ and based on a presentation by mathematician Richard Kramer at the National Center Center for Genome Resources in Santa Fe, NM.
Jean Constant - Julia set
Submitted by Jean Constant on
The Julia set is a set of complex numbers which do not converge to any limit when a given mapping is repeatedly applied to them (Oxford). The dynamic of the proposition was examined in the context of a finite two-dimensional surface.
Jean Constant - Fractals
Submitted by Jean Constant on
A fractal or — iterated function system — is an object or quantity that displays self-similarity on all scales (Wolfram). A minimal surface is a surface that has the smallest possible area for a surface spanning the boundary of that piece.
The object of that presentation was to evaluate how two opposite concepts could fit within the boundaries of a graphic visualization.
Jean Constant - Crystallographic points groups
Submitted by Jean Constant on
The Crystallographic point groups are point groups in which translational periodicity is required . There are 32 such groups.
Following is two example from a series on the 32 point groups template developed by Prof. Steve Dutch and that focus on the dynamic of the concept.