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  2. Lift (mathematics) - Wikipedia

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

    A basic example in topology is lifting a path in one topological space to a path in a covering space. [1] For example, consider mapping opposite points on a sphere to the same point, a continuous map from the sphere covering the projective plane. A path in the projective plane is a continuous map from the unit interval [0,1]. We can lift such a ...

  3. Topos - Wikipedia

    en.wikipedia.org/wiki/Topos

    More exotic examples, and the raison d'être of topos theory, come from algebraic geometry. The basic example of a topos comes from the Zariski topos of a scheme . For each scheme X {\displaystyle X} there is a site Open ( X ) {\displaystyle {\text{Open}}(X)} (of objects given by open subsets and morphisms given by inclusions) whose category of ...

  4. Closest pair of points problem - Wikipedia

    en.wikipedia.org/wiki/Closest_pair_of_points_problem

    The closest pair of points problem or closest pair problem is a problem of computational geometry: given points in metric space, find a pair of points with the smallest distance between them. The closest pair problem for points in the Euclidean plane [ 1 ] was among the first geometric problems that were treated at the origins of the systematic ...

  5. Euclidean algorithm - Wikipedia

    en.wikipedia.org/wiki/Euclidean_algorithm

    For example, 21 is the GCD of 252 and 105 (as 252 = 21 × 12 and 105 = 21 × 5), and the same number 21 is also the GCD of 105 and 252 − 105 = 147. Since this replacement reduces the larger of the two numbers, repeating this process gives successively smaller pairs of numbers until the two numbers become equal.

  6. Straightedge and compass construction - Wikipedia

    en.wikipedia.org/wiki/Straightedge_and_compass...

    For example, using a compass, straightedge, and a piece of paper on which we have the parabola y=x 2 together with the points (0,0) and (1,0), one can construct any complex number that has a solid construction. Likewise, a tool that can draw any ellipse with already constructed foci and major axis (think two pins and a piece of string) is just ...

  7. The 22 best Hanukkah gifts of 2024 - AOL

    www.aol.com/lifestyle/best-hanukkah-gifts-2024...

    Kids who like playing with traditional Magna-Tiles will love this set that looks like a Hanukkah-themed gingerbread house. Kids can use the 12 tiles to build a charming little snow covered house ...

  8. Parallelogram - Wikipedia

    en.wikipedia.org/wiki/Parallelogram

    The base pairs form a parallelogram with half the area of the quadrilateral, A q, as the sum of the areas of the four large triangles, A l is 2 A q (each of the two pairs reconstructs the quadrilateral) while that of the small triangles, A s is a quarter of A l (half linear dimensions yields quarter area), and the area of the parallelogram is A ...

  9. 10 of the Most Expensive Fines in Football - AOL

    www.aol.com/finance/10-most-expensive-fines...

    NFL players have sky-high salaries and contracts that would make the average person feel faint. They also get slapped with fines left and right, some frivolous and some substantial.