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The fold-and-cut theorem states that any shape with straight sides can be cut from a single (idealized) sheet of paper by folding it flat and making a single straight complete cut. [1] Such shapes include polygons, which may be concave, shapes with holes, and collections of such shapes (i.e. the regions need not be connected ).
Snowflakes that look identical, but may vary at the molecular level, have been grown under controlled conditions. [12] Although snowflakes are never perfectly symmetrical, the growth of a non-aggregated snowflake often approximates six-fold radial symmetry, arising from the hexagonal crystalline structure of ice. [13]
The snowflake schema is in the same family as the star schema logical model. In fact, the star schema is considered a special case of the snowflake schema. The snowflake schema provides some advantages over the star schema in certain situations, including: Some OLAP multidimensional database modeling tools are optimized for snowflake schemas. [3]
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The Koch snowflake (also known as the Koch curve, Koch star, or Koch island [1] [2]) is a fractal curve and one of the earliest fractals to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled "On a Continuous Curve Without Tangents, Constructible from Elementary Geometry" [3] by the Swedish mathematician Helge von Koch.
The major question about such crease patterns is whether a given crease pattern can be folded to a flat model, and if so, how to fold them; this is an NP-complete problem. [32] Related problems when the creases are orthogonal are called map folding problems. There are three mathematical rules for producing flat-foldable origami crease patterns ...
Arrange a rack in center of oven; preheat to 300°. Draw a 9" circle in the center of a piece of parchment, turn over, and place on a baking sheet. In the large bowl of a stand mixer fitted with ...
An n-flake, polyflake, or Sierpinski n-gon, [1]: 1 is a fractal constructed starting from an n-gon.This n-gon is replaced by a flake of smaller n-gons, such that the scaled polygons are placed at the vertices, and sometimes in the center.