Snowflake of ice. At that stage, the snowflake has the shape of a minute hexagon. The six "arms" of the snowflake, or dendrites, then grow independently from each of the corners of the hexagon, while either side of each arm grows independently. The microenvironment in which the snowflake grows changes dynamically as the snowflake falls through the cloud and tiny changes in temperature and humidity affect the way in which water molecules attach to the snowflake. Since the micro-environment (and its changes) are very nearly identical around the snowflake, each arm tends to grow in nearly the same way. However, being
Five points determine a conic the answer is given in terms of the multiset coefficient, more familiarly the binomial coefficient, or more elegantly the rising factorial, as: This is via the analogous analysis of the Veronese map: "k" points in general position impose "k" independent linear conditions on a variety (because the Veronese map is biregular), and the number of monomials of degree "d" in formula_18 variables ("n"-dimensional projective space has formula_18 homogeneous coordinates) is formula_20 from which 1 is subtracted because of projectivization: multiplying a polynomial by a constant does not change its zeros. In the above formula, the number of points "k" is