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IBM System/4 Pi, a family of avionics computers; 4Pi microscope, a microscope that uses interference and fluorescence computers; 4×π = 12.56637..., the solid angle of a complete sphere measured in steradians; Hermetic detector (also called a 4π detector)
The solid angle of a sphere measured from any point in its interior is 4 π sr. The solid angle subtended at the center of a cube by one of its faces is one-sixth of that, or 2 π /3 sr. The solid angle subtended at the corner of a cube (an octant) or spanned by a spherical octant is π /2 sr, one-eight of the solid angle of a sphere. [1]
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables . is the radius,
A History of Pi (book) Indiana Pi Bill; Leibniz formula for pi; Lindemann–Weierstrass theorem (Proof that π is transcendental) List of circle topics; List of formulae involving π; Liu Hui's π algorithm; Mathematical constant (sorted by continued fraction representation) Mathematical constants and functions; Method of exhaustion; Milü; Pi ...
where C is the circumference of a circle, d is the diameter, and r is the radius.More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width.
A 4Pi microscope is a laser scanning fluorescence microscope with an improved axial resolution.With it the typical range of the axial resolution of 500–700 nm can be improved to 100–150 nm, which corresponds to an almost spherical focal spot with 5–7 times less volume than that of standard confocal microscopy.
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It is used in three dimensional geometry, and is analogous to the radian, which quantifies planar angles. A solid angle in the form of a right circular cone can be projected onto a sphere, defining a spherical cap where the cone intersects the sphere. The magnitude of the solid angle expressed in steradians is defined as the quotient of the ...