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  2. New York Regents Examinations - Wikipedia

    en.wikipedia.org/wiki/New_York_Regents_Examinations

    Most Regents exams consist of a single three-hour testing period. The exception is the Earth Science exam, which consists of a 41-minute (approximate) laboratory component, known as the Earth Science lab practical, given around two weeks prior to the three-hour exam. The Regents exams are administered in January, June, and August.

  3. List of formulas in elementary geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    This is a list of volume formulas of basic shapes: [4]: 405–406 ... List of formulas in elementary geometry. 2 languages ...

  4. Geometrization conjecture - Wikipedia

    en.wikipedia.org/wiki/Geometrization_conjecture

    The third is the only example of a non-trivial connected sum with a geometric structure. This is the only model geometry that cannot be realized as a left invariant metric on a 3-dimensional Lie group. Finite volume manifolds with this geometry are all compact and have the structure of a Seifert fiber space (often in several ways). Under ...

  5. Volume form - Wikipedia

    en.wikipedia.org/wiki/Volume_form

    In other words, a volume form gives rise to a measure with respect to which functions can be integrated by the appropriate Lebesgue integral. The absolute value of a volume form is a volume element, which is also known variously as a twisted volume form or pseudo-volume form. It also defines a measure, but exists on any differentiable manifold ...

  6. Napkin ring problem - Wikipedia

    en.wikipedia.org/wiki/Napkin_ring_problem

    Lines, L. (1965), Solid geometry: With Chapters on Space-lattices, Sphere-packs and Crystals, Dover. Reprint of 1935 edition. A problem on page 101 describes the shape formed by a sphere with a cylinder removed as a "napkin ring" and asks for a proof that the volume is the same as that of a sphere with diameter equal to the length of the hole.

  7. Gabriel's horn - Wikipedia

    en.wikipedia.org/wiki/Gabriel's_horn

    Graph of = /. Gabriel's horn is formed by taking the graph of =, with the domain and rotating it in three dimensions about the x axis. The discovery was made using Cavalieri's principle before the invention of calculus, but today, calculus can be used to calculate the volume and surface area of the horn between x = 1 and x = a, where a > 1. [6]

  8. Truncated tetrahedron - Wikipedia

    en.wikipedia.org/wiki/Truncated_tetrahedron

    Given the edge length .The surface area of a truncated tetrahedron is the sum of 4 regular hexagons and 4 equilateral triangles' area, and its volume is: [2] =, =.. The dihedral angle of a truncated tetrahedron between triangle-to-hexagon is approximately 109.47°, and that between adjacent hexagonal faces is approximately 70.53°.

  9. Minkowski's theorem - Wikipedia

    en.wikipedia.org/wiki/Minkowski's_theorem

    Minkowski's theorem states that if the volume of S is strictly greater than 2 n d(L), then S must contain at least one lattice point other than the origin. (Since the set S is symmetric, it would then contain at least three lattice points: the origin 0 and a pair of points ± x , where x ∈ L \ 0 .)