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  2. Differential geometry of surfaces - Wikipedia

    en.wikipedia.org/wiki/Differential_geometry_of...

    The intrinsic geometry of this surface is now better understood in terms of the Poincaré metric on the upper half plane or the unit disc, and has been described by other models such as the Klein model or the hyperboloid model, obtained by considering the two-sheeted hyperboloid q(x, y, z) = −1 in three-dimensional Minkowski space, where q(x ...

  3. Euclidean geometry - Wikipedia

    en.wikipedia.org/wiki/Euclidean_geometry

    Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements.Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions from these.

  4. Greek mathematics - Wikipedia

    en.wikipedia.org/wiki/Greek_mathematics

    [10] [11] [8] Unlike the flourishing of Greek literature in the span of 800 to 600 BC, not much is known about Greek mathematics in this early period—nearly all of the information was passed down through later authors, beginning in the mid-4th century BC. [12] [13]

  5. Metric space - Wikipedia

    en.wikipedia.org/wiki/Metric_space

    Metric spaces are also studied in their own right in metric geometry [2] and analysis on metric spaces. [ 3 ] Many of the basic notions of mathematical analysis , including balls , completeness , as well as uniform , Lipschitz , and Hölder continuity , can be defined in the setting of metric spaces.

  6. Curvature - Wikipedia

    en.wikipedia.org/wiki/Curvature

    A migrating wild-type Dictyostelium discoideum cell whose boundary is colored by curvature. Scale bar: 5 μm. In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane.

  7. List of important publications in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_important...

    This 13th-century book contains the earliest complete solution of 19th-century Horner's method of solving high order polynomial equations (up to 10th order). It also contains a complete solution of Chinese remainder theorem, which predates Euler and Gauss by several centuries.

  8. Polyhedron - Wikipedia

    en.wikipedia.org/wiki/Polyhedron

    In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-) 'many' and ἕδρον (-hedron) 'base, seat') is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is a polyhedron that bounds a convex set.

  9. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    Algebra (and later, calculus) can thus be used to solve geometrical problems. Geometry was split into two new subfields: synthetic geometry, which uses purely geometrical methods, and analytic geometry, which uses coordinates systemically. [23] Analytic geometry allows the study of curves unrelated to circles and lines.

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