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In mathematics, hyperbolic functions are analogs of the ordinary trigonometric functions defined for the hyperbola rather than on the circle: just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the equilateral hyperbola.
Rev Dr James McCosh LLD was a prominent philosopher of the Scottish School of Common Sense. He was president of Princeton University 1868–88. McCosh Hall is named in his honour.
A catenoid is a type of surface, arising by rotating a catenary curve about an axis. It is a minimal surface, meaning that it occupies the least area when bounded by a closed space. It was formally described in 1744 by the mathematician Leonhard Euler.
In mathematics and physics, n-dimensional de Sitter space is a maximally symmetric Lorentzian manifold with constant positive scalar curvature. It is the Lorentzian analogue of an n-sphere.
Chebyshev filters are analog or digital filters having a steeper roll-off than Butterworth filters, and have passband ripple or stopband ripple. Chebyshev filters have the property that they minimize the error between the idealized and the actual filter characteristic over the range of the filter, but with ripples in the passband. This type of filter is named after Pafnuty Chebyshev because its mathematical characteristics are derived from Chebyshev polynomials. The type I Chebyshev filters are called usually as just "Chebyshev filters", the type II ones are usually called "inverse Chebyshev filters".
In the differential geometry of curves, a roulette is a kind of curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, and involutes.
Bipolar coordinates are a two-dimensional orthogonal coordinate system based on the Apollonian circles.. Confusingly, the same term is also sometimes used for two-center bipolar coordinates. There is also a third system, based on two poles.
In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane. It consists of three line segments called sides or edges and three points called angles or vertices.
In hyperbolic geometry, the angle of parallelism , is the angle at the non-right angle vertex of a right hyperbolic triangle having two asymptotic parallel sides. The angle depends on the segment length a between the right angle and the vertex of the angle of parallelism.
In physics and astronomy, Euler's three-body problem is to solve for the motion of a particle that is acted upon by the gravitational field of two other point masses that are fixed in space. This problem is exactly solvable, and yields an approximate solution for particles moving in the gravitational fields of prolate and oblate spheroids. This problem is named after Leonhard Euler, who discussed it in memoirs published in 1760. Important extensions and analyses were contributed subsequently by Lagrange, Liouville, Laplace, Jacobi, Darboux, Le Verrier, Velde, Hamilton, Poincaré, Birkhoff and E. T. Whittaker, among others.
In geometry, a Lambert quadrilateral, named after Johann Heinrich Lambert, is a quadrilateral in which three of its angles are right angles. Historically, the fourth angle of a Lambert quadrilateral was of considerable interest since if it could be shown to be a right angle, then the Euclidean parallel postulate could be proved as a theorem. It is now known that the type of the fourth angle depends upon the geometry in which the quadrilateral exists. In hyperbolic geometry the fourth angle is acute, in Euclidean geometry it is a right angle and in elliptic geometry it is an obtuse angle.
A Saccheri quadrilateral is a quadrilateral with two equal sides perpendicular to the base. It is named after Giovanni Gerolamo Saccheri, who used it extensively in his book Euclides ab omni naevo vindicatus first published in 1733, an attempt to prove the parallel postulate using the method Reductio ad absurdum.
In relativity, rapidity is commonly used as a measure for relativistic velocity. Mathematically, rapidity can be defined as the hyperbolic angle that differentiates two frames of reference in relative motion, each frame being associated with distance and time coordinates.
In geometry, the elliptic coordinate system is a two-dimensional orthogonal coordinate system in which the coordinate lines are confocal ellipses and hyperbolae. The two foci and are generally taken to be fixed at and , respectively, on the -axis of the Cartesian coordinate system.
Toroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional bipolar coordinate system about the axis that separates its two foci. Thus, the two foci and in bipolar coordinates become a ring of radius in the plane of the toroidal coordinate system; the -axis is the axis of rotation. The focal ring is also known as the reference circle.
Bispherical coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional bipolar coordinate system about the axis that connects the two foci. Thus, the two foci and in bipolar coordinates remain points in the bispherical coordinate system.
Cosh Boy is a 1953 British film noir directed by Lewis Gilbert and starring James Kenney and Joan Collins. It was made at Riverside Studios in Hammersmith.
Chris Cosh is an American football coach and former player. He currently serves as the defensive coordinator and defensive backs coach at the University of Delaware.
Scottish Common Sense Realism, also known as the Scottish School of Common Sense, is a realist school of philosophy that originated in the ideas of Scottish philosophers Thomas Reid, Adam Ferguson, James Beattie, and Dugald Stewart during the 18th-century Scottish Enlightenment. Reid emphasized man's innate ability to perceive common ideas and that this process is inherent in and interdependent with judgement. Common sense, therefore, is the foundation of philosophical inquiry. Though best remembered for its opposition to the pervasive philosophy of David Hume, Scottish Common Sense philosophy is influential and evident in the works of Thomas Jefferson and late 18th-century American politics.
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