Mathematics Education Art and Architecture: Representations of the Elliptic Paraboloid (original) (raw)
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2016
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The point and the line are simple geometric elements with immense creative capacity. They are the foundations on which the most complex geometries rest and therefore require detailed understanding and attention to achieve full mastery of them. The point and the line are totally connected with the space and the spatial coordinates; the adaptation of the geometric space to the shape facilitates the calculation and the geometric development. They are the basis of geometry, which floods the art world in all its expressions. Painting, sculpture, fashion or music use geometry as a source of inspiration, as an expression of their own being. This article seeks to unify the various existing approaches to reach these basic elements of geometry. Different languages: mathematics, drawing and art and other artistic expressions can define the same geometric object. Our approach is from the point of view of mathematics and contemporary art. Only by knowing these parallel approaches will we be able to master it, understand it and be able to use it freely, at will. This is the path that we seek our first-year Architecture students to follow. They need to master the bases of the form, sometimes very propaedeutic, but without which it would be impossible to establish the later complexity. For this reason, we close this article with three examples of projects carried out by the students, which illustrate the skills acquired and the validity of the method used for integrating knowledge.
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This paper illustrates a teaching setting which adopts a constructivist approach, and is centered on the combination of Mathematics and Art. The aim is to appeal to those minds that have a curiosity for a discipline which has long interacted with artistic expression, and to introduce new perspectives in the teaching of Mathematics in the light of the latest technological challenges. The trigger element - a decorative spiral frieze - has led to a process of Euclidean geometrical construction first with traditional tools, and then through the use of simple algorithms implemented in the MatCos programming environment. The drawing of the spiral curve represents a learning opportunity, a practice which combines analysis and synthesis, a journey between past and present which offers the student the opportunity to acquire some basic conceptual and instrumental implications in the age-old relationship between Mathematics and Art.