Abstract
This paper describes the methodology used by Atractor Association in its efforts to communicate ideas and relevant results of Mathematics to non-specialists. This description is illustrated with numerous examples of interactive exhibits, both virtual and non-virtual, created in the belief that interactivity is an important factor in the involvement of the target audience. Some examples of non-virtual exhibits, such as a large Ames Room, the three conical billiards or the slit hyperboloid, by their size or difficulty of construction are costly and require a large space; however others are quite simple and can easily be reproduced, even in small schools or groups. The list of examples of virtual exhibits, all produced by Atractor, ends with a reference to the DVD ‘Symmetry—the dynamical way’ and to the program GeCla, which allows the generation of friezes, patterns and rosettes and the assisted classification thereof, also including the possibility of competition via the Internet.
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Notes
- 1.
Using more technical language: every continuous vector field tangent to a sphere vanishes at least at one point.
- 2.
Not only in Portuguese, but also in English, French, German, Italian and Spanish.
- 3.
The solution consists of adding two points (at infinity) to the plane, each of which represents the point at infinity which corresponds to one of the two directions of a line that is perpendicular to the directions of the translations of the frieze. And the stamp consisting of the usual cylinder to which those two points are added is precisely a sphere. An animation shows how that (elongated) sphere, rotating around those two points, stamps an open spherical calotte, which is a model of the plane. With that rotation, if the direction is maintained, the stamp never returns to its initial position, therefore it is natural to say that the rotation is of infinite order. In the same way that it was natural for a rotation of order n to introduce the correction of −(1+1/n), here it is natural that the correction should be −1 for each of these points.
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© 2012 Springer-Verlag Berlin Heidelberg
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Arala Chaves, M. (2012). Atractor. In: Behrends, E., Crato, N., Rodrigues, J. (eds) Raising Public Awareness of Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25710-0_10
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DOI: https://doi.org/10.1007/978-3-642-25710-0_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25709-4
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