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THE HEXAGON. "The molecule H2O (water) contains one oxygen and two hydrogen. These two hydrogen atoms sit at an angle in relation to the oxygen which is perfectly the same angle as the corners of a hexagon, so building the lattice structure." http://thesmarthappyproject.com/hexagon-geometry-snowflake/ View in LinkedIn

SO ENDS my homage to Kepler's moment on the Charles Bridge in Prague. The mathematics of tiling tessellations from MC Escher transition through Kepler's snowflake to next weekend's Fragment on the geometry of spider webs. All three captured in a memorable moment on the Charles Bridge on the very anniversary of Kepler's birthday. With a fleck of snow on a black coat. A real treat linking radiant spots in time. View in LinkedIn

"THE KOCH SNOWFLAKE (also known as the Koch curve, Koch star, or Koch island) is a mathematical curve and one of the earliest fractal curves to have been described. The progression for the area of the snowflake converges to 8/5 times the area of the original triangle, while the progression for the snowflake's perimeter diverges to infinity. Consequently, the snowflake has a finite area bounded by an infinitely long line." https://en.wikipedia.org/wiki/Koch_snowflake View in LinkedIn

SIMPLICITY BENEATH. "Throughout the natural and artificial world one observes phenomena of great complexity...research in physics and to some extent biology and other fields have shown that the basic components of many systems are quite simple. It is now a crucial problem for many areas of science to elucidate the mathematical mechanisms by which large numbers of such simple components, acting together, can produce behavior of the great complexity observed." https://lnkd.in/dc_82je View in LinkedIn

THE NOTHING TREATISE ON A SNOWFLAKE. "Lacking the necessary funds to buy an appropriate Christmas gift for a friend, Kepler decided to write the essay on the snowflake. After all, he asked rhetorically, what do astronomers and mathematicians "who have Nothing and receive Nothing" have to give, but Nothing?" http://www.keplersdiscovery.com/SixCornered.html View in LinkedIn

SERIOUS SNOWFLAKE MATHEMATICS. How Kepler's "nothing" could demand such deep thinking to solve. Take a block of ice for this journey. https://lnkd.in/d6pKQyK View in LinkedIn

ON SNOWFLAKES AND VIRUS GEOMETRY, a ride on the wild side. Take a pinch of salt for this journey. https://lnkd.in/deFn7Te View in LinkedIn

TILING SHAPES. "Fibonacci snowflakes are somehow related to the Fibonacci fractals. They also form a subclass of tiles used for tiling the plane." https://lnkd.in/desvnVq View in LinkedIn

COMPLEMENTARY SHAPES. "Very cold? We get columns. Cold and high humidity? Dendrites. Cold and medium humidity? Sectored plates. Still, none of this explains how two separate arms can form complementary patterns." Nice graph of temperature vs form. http://www.itsokaytobesmart.com/post/72704847892/youve-watched-this-weeks-video-on-the-science View in LinkedIn

HALF TRUTH. "Snow crystals usually aren’t completely symmetrical. Instead, they are quite irregular and lumpy, full of conglomerations and corrections. The hexagonal crystal structure holds up in all cases, but the sort of perfect fractal sculpture you’ve been led to believe defines a snowflake? It’s a half-truth, at best." https://lnkd.in/dTbpCSB View in LinkedIn