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If K is a finite field of odd characteristic the absolute points also form a quadric, but if the characteristic is even the absolute points form a hyperplane (this is an example of a pseudo polarity). Under any duality, the point P is called the pole of the hyperplane P ⊥, and this hyperplane is called the polar of the point P. Using this ...
A wedge is a polyhedron of a rectangular base, with the faces are two isosceles triangles and two trapezoids that meet at the top of an edge. [1]. A prismatoid is defined as a polyhedron where its vertices lie on two parallel planes, with its lateral faces are triangles, trapezoids, and parallelograms; [2] the wedge is an example of prismatoid because of its top edge is parallel to the ...
This projection most commonly sights down a carbon-carbon bond, making it a very useful way to visualize the stereochemistry of alkanes. A Newman projection visualizes the conformation of a chemical bond from front to back, with the front atom represented by the intersection of three lines (a dot) and the back atom as a circle.
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.
Example of the use of descriptive geometry to find the shortest connector between two skew lines. The red, yellow and green highlights show distances which are the same for projections of point P. Given the X, Y and Z coordinates of P, R, S and U, projections 1 and 2 are drawn to scale on the X-Y and X-Z planes, respectively.
In normal aspect, pseudoconical projections represent the central meridian as a straight line, other meridians as complex curves, and parallels as circular arcs. Azimuthal In standard presentation, azimuthal projections map meridians as straight lines and parallels as complete, concentric circles. They are radially symmetrical.
Simple examples. A simple example of a regular surface is given by the 2-sphere {(x, y, z) | x 2 + y 2 + z 2 = 1}; this surface can be covered by six Monge patches (two of each of the three types given above), taking h(u, v) = ± (1 − u 2 − v 2) 1/2. It can also be covered by two local parametrizations, using stereographic projection.
In a hydrocarbon molecule with all carbon atoms making up the backbone in a tetrahedral molecular geometry, the zigzag backbone is in the paper plane (chemical bonds depicted as solid line segments) with the substituents either sticking out of the paper toward the viewer (chemical bonds depicted as solid wedges) or away from the viewer ...