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  2. Euler characteristic - Wikipedia

    en.wikipedia.org/wiki/Euler_characteristic

    This equation, stated by Euler in 1758, [2] is known as Euler's polyhedron formula. [3] It corresponds to the Euler characteristic of the sphere (i.e. = ), and applies identically to spherical polyhedra. An illustration of the formula on all Platonic polyhedra is given below.

  3. Euler characteristic of an orbifold - Wikipedia

    en.wikipedia.org/wiki/Euler_characteristic_of_an...

    (The appearance of in the summation is the usual Euler characteristic.) [1] [2] If the action is free, the sum has only a single term, and so this expression reduces to the topological Euler characteristic of divided by | |. [2]

  4. Local Euler characteristic formula - Wikipedia

    en.wikipedia.org/wiki/Local_Euler_characteristic...

    In the mathematical field of Galois cohomology, the local Euler characteristic formula is a result due to John Tate that computes the Euler characteristic of the group cohomology of the absolute Galois group G K of a non-archimedean local field K.

  5. Riemann–Hurwitz formula - Wikipedia

    en.wikipedia.org/wiki/Riemann–Hurwitz_formula

    Indeed, to obtain this formula, remove disjoint disc neighborhoods of the branch points from S and their preimages in S' so that the restriction of is a covering. Removing a disc from a surface lowers its Euler characteristic by 1 by the formula for connected sum, so we finish by the formula for a non-ramified covering.

  6. Euler class - Wikipedia

    en.wikipedia.org/wiki/Euler_class

    In mathematics, specifically in algebraic topology, the Euler class is a characteristic class of oriented, real vector bundles. Like other characteristic classes, it measures how "twisted" the vector bundle is. In the case of the tangent bundle of a smooth manifold, it generalizes the classical notion of Euler characteristic.

  7. Will it snow today? Millions under winter storm watches ... - AOL

    www.aol.com/snow-today-millions-under-winter...

    Millions in the eastern U.S. continued to get their first real taste of winter weather on Friday with a storm that's bringing rain and up to a foot of snow to higher elevations. Light snow could ...

  8. Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Euler's_formula

    Euler's formula is ubiquitous in mathematics, physics, chemistry, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics". [2] When x = π, Euler's formula may be rewritten as e iπ + 1 = 0 or e iπ = −1, which is known as Euler's identity.

  9. We found 14 personalized gifts from Walmart that look more ...

    www.aol.com/lifestyle/we-found-14-personalized...

    Personalized gifts don't have to be expensive or purchased months in advance. Give a thoughtful gift from Walmart this year, starting at just $5.