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  2. Unit hyperbola - Wikipedia

    en.wikipedia.org/wiki/Unit_hyperbola

    The unit hyperbola is blue, its conjugate is green, and the asymptotes are red. In geometry, the unit hyperbola is the set of points (x,y) in the Cartesian plane that satisfy the implicit equation = In the study of indefinite orthogonal groups, the unit hyperbola forms the basis for an alternative radial length

  3. Hyperbola - Wikipedia

    en.wikipedia.org/wiki/Hyperbola

    Here a = b = 1 giving the unit hyperbola in blue and its conjugate hyperbola in green, sharing the same red asymptotes. ... In a unit circle, the angle ...

  4. Group of rational points on the unit circle - Wikipedia

    en.wikipedia.org/wiki/Group_of_rational_points...

    For the group on the unit circle, the appropriate subgroup is the subgroup of points of the form (w, x, 1, 0), with + =, and its identity element is (1, 0, 1, 0). The unit hyperbola group corresponds to points of form (1, 0, y, z), with =, and the identity is again (1, 0, 1, 0). (Of course, since they are subgroups of the larger group, they ...

  5. Hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_functions

    A ray through the unit hyperbola x 2 − y 2 = 1 at the point (cosh a, sinh a), where a is twice the area between the ray, the hyperbola, and the x-axis. For points on the hyperbola below the x-axis, the area is considered negative (see animated version with comparison with the trigonometric (circular) functions).

  6. Hyperbolic angle - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_angle

    Arcs with an angular magnitude on a circle generate a measure on certain measurable sets on the circle whose magnitude does not vary as the circle turns or rotates. For the hyperbola the turning is by squeeze mapping, and the hyperbolic angle magnitudes stay the same when the plane is squeezed by a mapping (x, y) ↦ (rx, y / r), with r > 0 .

  7. Today’s NYT ‘Strands’ Hints, Spangram and Answers for ...

    www.aol.com/today-nyt-strands-hints-spangram...

    Theme words stay highlighted in blue when found. Drag or tap letters to create words. If tapping, double tap the last letter to submit. Theme words fill the board entirely. No theme words overlap.

  8. Caps revealed for Hall of Fame Class of 2025 plaques - AOL

    www.aol.com/caps-revealed-hall-fame-class...

    The seven-time All-Star also played for the Cincinnati Reds (1984-87), Oakland Athletics (1988-89), Brewers (1990), California Angels (1991) and Toronto Blue Jays (1991).

  9. Eccentricity (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Eccentricity_(mathematics)

    A family of conic sections of varying eccentricity share a focus point and directrix line, including an ellipse (red, e = 1/2), a parabola (green, e = 1), and a hyperbola (blue, e = 2). The conic of eccentricity 0 in this figure is an infinitesimal circle centered at the focus, and the conic of eccentricity ∞ is an infinitesimally separated ...