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  2. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    Berger–Kazdan comparison theorem (Riemannian geometry) Bernstein's theorem (approximation theory) Bernstein's theorem (functional analysis) Berry–Esséen theorem (probability theory) Bertini's theorem (algebraic geometry) Bertrand–Diquet–Puiseux theorem (differential geometry) Bertrand's ballot theorem (probability theory, combinatorics)

  3. Straightedge and compass construction - Wikipedia

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

    The basic constructions. All straightedge-and-compass constructions consist of repeated application of five basic constructions using the points, lines and circles that have already been constructed. These are: Creating the line through two points; Creating the circle that contains one point and has a center at another point

  4. Difference of two squares - Wikipedia

    en.wikipedia.org/wiki/Difference_of_two_squares

    Another geometric proof proceeds as follows: We start with the figure shown in the first diagram below, a large square with a smaller square removed from it. The side of the entire square is a, and the side of the small removed square is b. The area of the shaded region is . A cut is made, splitting the region into two rectangular pieces, as ...

  5. List of formulas in elementary geometry - Wikipedia

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

    The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),

  6. Constructible polygon - Wikipedia

    en.wikipedia.org/wiki/Constructible_polygon

    In order to reduce a geometric problem to a problem of pure number theory, the proof uses the fact that a regular n-gon is constructible if and only if the cosine ⁡ (/) is a constructible number—that is, can be written in terms of the four basic arithmetic operations and the extraction of square roots.

  7. Birkhoff's axioms - Wikipedia

    en.wikipedia.org/wiki/Birkhoff's_axioms

    These postulates are all based on basic geometry that can be confirmed experimentally with a scale and protractor. Since the postulates build upon the real numbers, the approach is similar to a model-based introduction to Euclidean geometry. Birkhoff's axiomatic system was utilized in the secondary-school textbook by Birkhoff and Beatley. [2]

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