Prismatic surface

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A prismatic surface is a surface generated by all the lines that are parallel to a given line and intersect a broken line that is not in the same plane as the given line. [1] The broken line is the directrix of the surface; the parallel lines are its generators (or elements). If the broken line is closed (i.e., a closed polygon), then the surface is a closed prismatic surface.

In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel. However, two lines in three-dimensional space which do not meet must be in a common plane to be considered parallel; otherwise they are called skew lines. Parallel planes are planes in the same three-dimensional space that never meet.

Line (geometry) straight object with negligible width and depth

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects. Until the 17th century, lines were defined as the "[…] first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which […] will leave from its imaginary moving some vestige in length, exempt of any width. […] The straight line is that which is equally extended between its points."

Plane (geometry) Flat, two-dimensional surface

In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far. A plane is the two-dimensional analogue of a point, a line and three-dimensional space. Planes can arise as subspaces of some higher-dimensional space, as with a room's walls extended infinitely far, or they may enjoy an independent existence in their own right, as in the setting of Euclidean geometry.

With regards to crystallography, a prismatic surface is a single face of a prismatic form, which is an open form consisting of three, four, or six identical faces related by a symmetry operator.[ citation needed ]

Crystallography The scientific study of crystal structure

Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. The word "crystallography" derives from the Greek words crystallon "cold drop, frozen drop", with its meaning extending to all solids with some degree of transparency, and graphein "to write". In July 2012, the United Nations recognised the importance of the science of crystallography by proclaiming that 2014 would be the International Year of Crystallography. X-ray crystallography is used to determine the structure of large biomolecules such as proteins. Before the development of X-ray diffraction crystallography, the study of crystals was based on physical measurements of their geometry. This involved measuring the angles of crystal faces relative to each other and to theoretical reference axes, and establishing the symmetry of the crystal in question. This physical measurement is carried out using a goniometer. The position in 3D space of each crystal face is plotted on a stereographic net such as a Wulff net or Lambert net. The pole to each face is plotted on the net. Each point is labelled with its Miller index. The final plot allows the symmetry of the crystal to be established.

In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.

See also

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In archaeology, a prismatic blade is a long, narrow, specialized stone flake tool with a sharp edge, like a small razor blade. Prismatic blades are flaked from stone cores through pressure flaking or direct percussion. This process results in a very standardized finished tool and waste assemblage. The most famous and most prevalent prismatic blade material is obsidian, as obsidian use was widespread in Mesoamerica, though chert, flint, and chalcedony blades are not uncommon. The term is generally restricted to Mesoamerican archeology, although some examples are found in the Old World, for example in a Minoan grave in Crete.

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Point at infinity Wikimedia disambiguation page

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Real projective plane

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Skew lines

In three-dimensional geometry, skew lines are two lines that do not intersect and are not parallel. A simple example of a pair of skew lines is the pair of lines through opposite edges of a regular tetrahedron. Two lines that both lie in the same plane must either cross each other or be parallel, so skew lines can exist only in three or more dimensions. Two lines are skew if and only if they are not coplanar.

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Elongated triangular tiling

In geometry, the elongated triangular tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex. It is named as a triangular tiling elongated by rows of squares, and given Schläfli symbol {3,6}:e.

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Computer representation of surfaces

In technical applications of 3D computer graphics (CAx) such as computer-aided design and computer-aided manufacturing, surfaces are one way of representing objects. The other ways are wireframe and solids. Point clouds are also sometimes used as temporary ways to represent an object, with the goal of using the points to create one or more of the three permanent representations.

References

  1. ↑ Velichová, Daniela. "Views of pyramidal (prismatic) surfaces". Slovenia: European Virtual Laboratory of Mathematics . Retrieved 11 June 2013.External link in |publisher= (help)
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