More Mathematical Objects
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FractalsWhat is there to say aside from the idea that even our understanding of eveything seems to be fractal in nature? |
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Hans Hinterreiter and Projective GeometryIn older literature, projective geometry is sometimes called 'higher geometry,' 'geometry of position', or 'descriptive geometry' (Cremona 1960, pp. v-vi). In the case of Hans Hinterreiter, after designing a simple square-based tiling, he gathered each set of parallel lines from the square grid at a point inside the field of the painting and voilá! |
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Moiré and HolographyHolograms can be conceived as moiré patterns (interference patterns) which have been harnessed into a figurative representation. They are a tribute to our organ of sight which interprets visual input into recognition. But do we do that with all our perceptions? There is a stream of thought that addresses this very question. |
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Pandora, or what is the Curvature of Space?You can prove mathematically that regular icosahedra do not fill space, but if space is curved, shouldn't there be a size of icosahedron that will match the curvature and then tile? If we can find the size at which this works, we will know the curvature of space, no? |
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Ruled Surfaces, Minimal Surfaces and Surfaces of RevolutionIf you remove the restriction of the flatness of the surface, you enter a whole new world where curves and straight lines are rotated about themselves and other points, travel along trajectories and spaces acquire all kinds of strange properties. For example, what does the surface look like that is made of s straight line rotating around itself at the same time as it is travelling in a perpendicular direction? |
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The Topology of ChainsAll chains have in common that they are made up of a repetition of rigid elements which, in combination, form a flexible connection. But if they were all suddenly turned into tear resistant but flexible rubber, not all would still remain attached. Some chains are simply or multiply linked tori, but some are linked in very unexpected ways, relying on the rigidity of their material. |