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Macro photography of a natural snowflake. A snowflake is a single ice crystal that is large enough to fall through the Earth's atmosphere as snow. [1] [2] [3] Snow appears white in color despite being made of clear ice. This is because the many small crystal facets of the snowflakes scatter the sunlight between them. [4]
A snowflake consists of roughly 10 19 water molecules which are added to its core at different rates and in different patterns depending on the changing temperature and humidity within the atmosphere that the snowflake falls through on its way to the ground. As a result, snowflakes differ from each other though they follow similar patterns. [17 ...
The hexagonal snowflake, a crystalline formation of ice, has intrigued people throughout history. This is a chronology of interest and research into snowflakes. Artists, philosophers, and scientists have wondered at their shape, recorded them by hand or in photographs, and attempted to recreate hexagonal snowflakes.
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.
A fourth-stage Gosper curve The line from the red to the green point shows a single step of the Gosper curve construction. The Gosper curve, named after Bill Gosper, also known as the Peano-Gosper Curve [1] and the flowsnake (a spoonerism of snowflake), is a space-filling curve whose limit set is rep-7.
All of the sides are equal to 2r because all of the sides are formed by two spheres touching. The height of which or the z -coordinate difference between the two "planes" is √ 6 r 2 / 3 . This, combined with the offsets in the x and y -coordinates gives the centers of the first row in the B plane:
A right star antiprism has two congruent coaxial regular convex or star polygon base faces, and 2n isosceles triangle side faces. Any star antiprism with regular convex or star polygon bases can be made a right star antiprism (by translating and/or twisting one of its bases, if necessary).
The Koch snowflake is irrep-7: six small snowflakes of the same size, together with another snowflake with three times the area of the smaller ones, can combine to form a single larger snowflake. A right triangle with side lengths in the ratio 1:2 is rep-5, and its rep-5 dissection forms the basis of the aperiodic pinwheel tiling.