e-book The Second Golden Rule

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  1. Golden Rule
  2. Golden Rule Chronology
  3. Bible Living

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Take the arrangement of leaves on the stem of a plant. As each new leaf grows, it does so at an angle offset from that of the leaf below. The most com mon angle between successive leaves is Why does the golden ratio play a role in the arrangement of leaves?

It's all down to the "irrationality" of the number. This can be said more precisely. Irrational numbers can be expressed as continued fractions - basically an infinite series of ever-diminishing terms. As each successive term is added, the continued fraction converges towards a single value. This turns out to be the key property.

Golden Rule

A new leaf must collect sunlight without throwing the leaves below it into too much shadow. A plant must arrange its leaves in such a way that the greatest number can spiral around the stem before a new leaf sprouts immediately above a lower one - that is offset at The golden ratio also crops up in the hard sciences. Take the growth of "quasi-crystals". These have "five-fold symmetry", which means they make a pattern that looks the same when rotated by multiples of one-fifth of In the s, physicists in Switzerland and the US imaged the microscopic terrain of the surface of such crystals.

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They found flat "terraces" punctuated by abrupt vertical steps. In many physical situations the transition probability is of the form.

Human - Golden Rule

The general form of Fermi's golden rule can apply to atomic transitions, nuclear decay, scattering A transition will proceed more rapidly if the coupling between the initial and final states is stronger. This coupling term is traditionally called the "matrix element" for the transition: The matrix element can be placed in the form of an integral where the interaction which causes the transition is expressed as a potential V which operates on the initial state wavefunction.

The transition probability is proportional to the square of the integral of this interaction over all of the space appropriate to the problem. Like Moray eels and Goby Fish. Or sea turtles and cleaning fish. You must write for your audience, but you do that by calculating the meaning of every word for maximum effect. How do you write for your audience?

Golden Rule Chronology

Depends on who you are writing for…. Write for yourself then. This applies directly to journals. If you keep a journal, do it right. Write to inform yourself.

Bible Living

Then you better follow the prompt they give you. Every essay and paper has a prompt, follow it. Learn what your professor wants. Every teacher has biases; gear your paper to those biases. Like the professor, you better read and reread the contest rules. They can be specific.