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  2. Honeycomb conjecture - Wikipedia

    en.wikipedia.org/wiki/Honeycomb_conjecture

    It is also related to the densest circle packing of the plane, in which every circle is tangent to six other circles, which fill just over 90% of the area of the plane. The case when the problem is restricted to a square grid was solved in 1989 by Jaigyoung Choe who proved that the optimal figure is an irregular hexagon. [4] [5]

  3. Shoelace formula - Wikipedia

    en.wikipedia.org/wiki/Shoelace_formula

    Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]

  4. William Delbert Gann - Wikipedia

    en.wikipedia.org/wiki/William_Delbert_Gann

    William Delbert Gann (June 6, 1878 – June 18, 1955) or WD Gann, was a finance trader who developed the technical analysis methods like the Gann angles [1] [2] and the Master Charts, [3] [4] where the latter is a collective name for his various tools like the Spiral Chart (also called the Square of Nine), [5] [6] [7] the Hexagon Chart, [8] and the Circle of 360.

  5. Apothem - Wikipedia

    en.wikipedia.org/wiki/Apothem

    Apothem of a hexagon Graphs of side, s; apothem, a; and area, A of regular polygons of n sides and circumradius 1, with the base, b of a rectangle with the same area. The green line shows the case n = 6. The apothem (sometimes abbreviated as apo [1]) of a regular polygon is a line segment from the center to the midpoint of one of its sides.

  6. Area formula (geometric measure theory) - Wikipedia

    en.wikipedia.org/wiki/Area_formula_(geometric...

    In geometric measure theory the area formula relates the Hausdorff measure of the image of a Lipschitz map, while accounting for multiplicity, to the integral of the Jacobian of the map. It is one of the fundamental results of the field that has connections, for example, to rectifiability and Sard's theorem .

  7. Pascal's theorem - Wikipedia

    en.wikipedia.org/wiki/Pascal's_theorem

    A short elementary proof of Pascal's theorem in the case of a circle was found by van Yzeren (1993), based on the proof in (Guggenheimer 1967). This proof proves the theorem for circle and then generalizes it to conics. A short elementary computational proof in the case of the real projective plane was found by Stefanovic (2010).

  8. Heron's formula - Wikipedia

    en.wikipedia.org/wiki/Heron's_formula

    The formula is credited to Heron (or Hero) of Alexandria (fl. 60 AD), [4] and a proof can be found in his book Metrica. Mathematical historian Thomas Heath suggested that Archimedes knew the formula over two centuries earlier, [ 5 ] and since Metrica is a collection of the mathematical knowledge available in the ancient world, it is possible ...

  9. Flexagon - Wikipedia

    en.wikipedia.org/wiki/Flexagon

    Figure 3 shows the first fold, and figure 4 the result of the first nine folds, which form a spiral. Figures 5-6 show the final folding of the spiral to make a hexagon; in 5, two red faces have been hidden by a valley fold, and in 6, two red faces on the bottom side have been hidden by a mountain fold.