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Principal symbol. The variation formula computations above define the principal symbol of the mapping which sends a pseudo-Riemannian metric to its Riemann tensor, Ricci tensor, or scalar curvature. The principal symbol of the map assigns to each a map from the space of symmetric (0,2)-tensors on to the space of (0,4)-tensors on given by.
Prentice's rule, named so after the optician Charles F. Prentice, is a formula used to determine the amount of induced prism in a lens: = where: P is the amount of prism correction (in prism dioptres) c is decentration (the distance between the pupil centre and the lens's optical centre, in millimetres)
The fundamental theorem of Riemannian geometry can be viewed as saying that this linear system has a unique solution. This is seen via the following computation: [14] in which the metric-compatibility condition is used three times for the first equality and the torsion-free condition is used three times for the second equality.
In geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical properties such as length. There are four types: translations, rotations, reflections, and glide reflections (see below ยง Classification ). The set of Euclidean plane isometries forms a ...
This article summarizes equations used in optics, including geometric optics, physical optics, radiometry, diffraction, and interferometry.
Truncation (geometry) Truncated square is a regular octagon: t {4} = {8} =. Truncated cube. t {4,3} or. Truncated cubic honeycomb. t {4,3,4} or. In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex.
Geometry. 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.
Convergence insufficiency. Convergence Insufficiency. Other names. Convergence disorder. Specialty. Ophthalmology, optometry. Convergence insufficiency is a sensory and neuromuscular anomaly of the binocular vision system, characterized by a reduced ability of the eyes to turn towards each other, or sustain convergence .
Esophoria is an eye condition involving inward deviation of the eye, usually due to extra-ocular muscle imbalance. It is a type of heterophoria. Cause. Causes include: Refractive errors; Divergence insufficiency; Convergence excess; this can be due to nerve, muscle, congenital or mechanical anomalies.
General theorem about nested parallelograms. The theorem of gnomon is special case of a more general statement about nested parallelograms with a common diagonal. For a given parallelogram consider an arbitrary inner parallelogram having as a diagonal as well.