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The Goldmann perimeter is a hollow white spherical bowl positioned a set distance in front of the patient. [3] An examiner presents a test light of variable size and intensity. The light may move towards the center from the perimeter (kinetic perimetry), or it may remain in one location (static perimetry).
Isoperimetric literally means "having the same perimeter". Specifically, the isoperimetric inequality states, for the length L of a closed curve and the area A of the planar region that it encloses, that , and that equality holds if and only if the curve is a circle.
Alternatively, the shape's area could be compared to that of its bounding circle, [1] [2] its convex hull, [1] [3] or its minimum bounding box. [3] Similarly, a comparison can be made between the perimeter of the shape and that of its convex hull, [3] its bounding circle, [1] or a circle having the same area. [1]
In Euclidean geometry, Brahmagupta's formula, named after the 7th century Indian mathematician, is used to find the area of any convex cyclic quadrilateral (one that can be inscribed in a circle) given the lengths of the sides. Its generalized version, Bretschneider's formula, can be used with non-cyclic quadrilateral.
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.
A circle packing for a five-vertex planar graph. The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible tangency relations between circles in the plane whose interiors are disjoint. A circle packing is a connected collection of circles (in general, on any Riemann surface) whose interiors are ...
Pilots use aeronautical charts based on LCC because a straight line drawn on a Lambert conformal conic projection approximates a great-circle route between endpoints for typical flight distances. The US systems of VFR ( visual flight rules ) sectional charts and terminal area charts are drafted on the LCC with standard parallels at 33°N and 45°N.
More formulas of this nature can be given, as explained by Ramanujan's theory of elliptic functions to alternative bases. Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function τ {\displaystyle \tau } and the Fourier coefficients j {\displaystyle \mathrm {j} } of the J-invariant ...