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  2. Hyperbola - Wikipedia

    en.wikipedia.org/wiki/Hyperbola

    Hyperbola (red): features. In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

  3. Hyperbolic trajectory - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_trajectory

    The blue path in this image is an example of a hyperbolic trajectory. A hyperbolic trajectory is depicted in the bottom-right quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the hyperbolic trajectory is shown in red. The height of the kinetic energy decreases ...

  4. Hyperbolic sector - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_sector

    A hyperbolic sector is a region of the Cartesian plane bounded by a hyperbola and two rays from the origin to it. For example, the two points (a, 1/a) and (b, 1/b) on the rectangular hyperbola xy = 1, or the corresponding region when this hyperbola is re-scaled and its orientation is altered by a rotation leaving the center at the origin, as with the unit hyperbola.

  5. Hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_functions

    Circle and hyperbola tangent at (1,1) display geometry of circular functions in terms of circular sector area u and hyperbolic functions depending on hyperbolic sector area u. The hyperbolic functions represent an expansion of trigonometry beyond the circular functions. Both types depend on an argument, either circular angle or hyperbolic angle.

  6. Hyperbolic geometry - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_geometry

    For example, two points uniquely define a line, and line segments can be infinitely extended. Two intersecting lines have the same properties as two intersecting lines in Euclidean geometry. For example, two distinct lines can intersect in no more than one point, intersecting lines form equal opposite angles, and adjacent angles of intersecting ...

  7. Hyperbolic angle - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_angle

    In mathematics, hyperbolic angle is an invariant measure as it is preserved under hyperbolic rotation. The hyperbola xy = 1 is rectangular with semi-major axis 2 {\displaystyle {\sqrt {2}}} , analogous to the circular angle equaling the area of a circular sector in a circle with radius 2 {\displaystyle {\sqrt {2}}} .

  8. 50 common hyperbole examples to use in your everyday life

    www.aol.com/news/50-common-hyperbole-examples...

    Ahead, we’ve rounded up 50 holy grail hyperbole examples — some are as sweet as sugar, and some will make you laugh out loud. 50 common hyperbole examples I’m so hungry, I could eat a horse.

  9. Hyperbolic coordinates - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_coordinates

    For example, in thermodynamics the isothermal process explicitly follows the hyperbolic path and work can be interpreted as a hyperbolic angle change. Similarly, a given mass M of gas with changing volume will have variable density δ = M / V , and the ideal gas law may be written P = k T δ so that an isobaric process traces a hyperbola in the ...