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For instance, while all the cross-sections of a ball are disks, [2] the cross-sections of a cube depend on how the cutting plane is related to the cube. If the cutting plane is perpendicular to a line joining the centers of two opposite faces of the cube, the cross-section will be a square, however, if the cutting plane is perpendicular to a ...
A 4K UHD 3D Mandelbulb video A ray-marched image of the 3D Mandelbulb for the iteration v ↦ v 8 + c. The Mandelbulb is a three-dimensional fractal, constructed for the first time in 1997 by Jules Ruis and further developed in 2009 by Daniel White and Paul Nylander using spherical coordinates.
A stone pillar in the 6th-century Marundeeswarar Temple in India shows three equilateral triangles rotated from each other to form a regular enneagram; like the Borromean rings these three triangles are linked and not pairwise linked, [12] but this crossing pattern describes a different link than the Borromean rings. [13]
In the mathematical field of topology, a section (or cross section) [1] of a fiber bundle is a continuous right inverse of the projection function. In other words, if E {\displaystyle E} is a fiber bundle over a base space , B {\displaystyle B} :
Vicsek fractal (5th iteration of cross form) In mathematics the Vicsek fractal, also known as Vicsek snowflake or box fractal, [1] [2] is a fractal arising from a construction similar to that of the Sierpiński carpet, proposed by Tamás Vicsek. It has applications including as compact antennas, particularly in cellular phones.
A necessary and sufficient condition for (, /,,) to form a fiber bundle is that the mapping admits local cross-sections (Steenrod 1951, §7). The most general conditions under which the quotient map will admit local cross-sections are not known, although if G {\displaystyle G} is a Lie group and H {\displaystyle H} a closed subgroup (and thus a ...
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In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations.This means that, compared to elementary Euclidean geometry, projective geometry has a different setting (projective space) and a selective set of basic geometric concepts.
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