linkedin post 2017-01-01 09:03:56

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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
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linkedin post 2017-01-02 07:18:50

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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
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linkedin post 2017-01-02 07:13:44

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"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
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linkedin post 2017-01-02 07:10:05

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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
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linkedin post 2017-01-02 07:03:54

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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
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linkedin post 2017-01-04 06:10:14

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COMMONALITY ENSURED. "Unicellular bottlenecks are present in distantly related multicellular lineages, and appear to be a critical step in the evolution of multicellular complexity. The unicellular bottleneck limits genetic diversity, and hence genetic conflict, among the cells of extant multicellular organisms, and ensures that all cells constituting a multicellular individual share a common developmental history and environment." https://lnkd.in/dU8HRX5 View in LinkedIn
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linkedin post 2017-01-04 06:06:44

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HYPOTHESIS. "More broadly, our finding that simple multicellularity can evolve in less than a year in both Chlamydomonas and Saccharomyces suggests that genetic barriers (for example, few mutational paths to multicellularity) may be less restrictive than ecological barriers, namely a lack of persistent selective advantages for cellular clusters." https://lnkd.in/dU8HRX5 View in LinkedIn
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linkedin post 2017-01-06 05:16:59

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NECESSARY BUT NOT SUFFICIENT. "Although epigenetic regulation was likely a necessary precondition for the emergence of multicellular organization (at least in extant lineages), it does not necessitate that such a transition from unicellularity to multicellularity will occur or explain how it occurs." https://lnkd.in/dTS7dFy View in LinkedIn
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