An Appeal To The Craft
Let
me count the ways,
I –
I –
– (Can you help me
quick-tongued
sharp-witted
sharp-witted
keen-minded teacher?)
Instruct me in your craft
so that I may discern
the metaphor in the reddening
of the Autumn leaves
the clouds of
approaching winter
the discarded rain-soaked
junk on the city streets.
so that I may discern
the metaphor in the reddening
of the Autumn leaves
the clouds of
approaching winter
the discarded rain-soaked
junk on the city streets.
They
told me to read
as much as possible
the works of Greater Writers
and by the action of Osmosis
I would absorb their words –
but my fingertips are not porous.
as much as possible
the works of Greater Writers
and by the action of Osmosis
I would absorb their words –
but my fingertips are not porous.
Show me the sum
of your vast experience
explain how
it adds up to a
prime number
curves into
the Golden Ratio.
of your vast experience
explain how
it adds up to a
prime number
curves into
the Golden Ratio.
Teach me, so I
may leave behind
something never
before said,
a bugle call never
before heard
in the hunt-like game
of this maddening pursuit.
may leave behind
something never
before said,
a bugle call never
before heard
in the hunt-like game
of this maddening pursuit.
I write these words,
but the ink is running out.
but the ink is running out.
I should probably get a new pen.
Newton -- William Blake
The Golden Mean (Golden Section, Sectio Aurea, Golden Ratio, Golden Number, Divine Proportion, Golden Proportion, Fibonacci Number, Phi, Extreme Ratio, Mean Ratio, Medial Section, Divine Proportion, Divine Section, Sectio Divina, Golden Cut) is a mathematical ratio (1:1.618) commonly found in natural patterns such as the spiral arrangement of leaves and other plant parts. It was apparently an element in the construction of the Egyptian pyramids and the Parthenon’s statues of Phidias in the 5th century BCE. At about the same time Platon described the five regular solids (the tetrahedron, cube, octahedron, dodecahedron, and icosahedron), some of which are related to the golden ratio. Its properties have been studied since the 4th-century-BCE mathematician Euclid (Eukleidēs, "renowned, glorious"), including its appearance in the dimensions of a regular pentagon and in a golden rectangle (which may be cut into a square and a smaller rectangle with the same aspect ratio); Euclid provided its earliest definition and employed it in several theorems and their proofs. In the 13th century Leonardo of Pisa (nicknamed "Fibonacci" [short for "filius Bonacci," son of the Bonacci"] in 1838 by the French historian Guillaume Libri; later in the century Édouard Lucas christened the “Fibonacci sequence), who popularized Arabic (actually Indian) numerals in Europe, introduced the “Fibonacci sequence,” which approaches the golden ratio asymptotically. (The sequence had been known to Indian mathematics since the 6th century.) The French historian Guillaume Libri nicknamed Leonardo "Fibonacci" [short for "filius Bonacci," son of the Bonacci"] in 1838, and later in the century Édouard Lucas christened the “Fibonacci sequence. In 1509 Luca de Pacioli, the Franciscan monk who codified the double-entry bookkeeping system used in Genova since 1340 (but had been independently developed a few centuries earlier in Goryeo [modern Korea]), applied its mathematics to architecture; Leonardo da Vinci, while he lived with and took mathematics lessons from Pacioli, drew the first illustrations of skeletonic solids, which allow an easy distinction between front and back. However, its decimal approximation was not revealed until 1597 when Michael Maestlin informed his former student Johannes Kepler in a letter. Kepler himself proved that the golden ratio is the limit of the ratio of consecutive Fibonacci numbers. (He claimed that the Pythagorean theorem was “a measure of gold” and the golden ratio was “a precious jewel.”) Martin Ohm was the first to use the term “goldener Schnitt” (golden section) to describe this ratio, in 1835, but in 1909 Mark Barr suggested the Greek letter phi (φ), the initial letter Phidias's name, as its symbol. Roger Penrose in 1974 discovered the Penrose tiling, a pattern that is related to the golden ratio both in the ratio of areas of its two rhombic tiles and in their relative frequency within the pattern, which led to new discoveries about quasicrystals. Many artists and architects, from the leading renaissance figures to moderns such as Le Corbusier and Salvador Dalí, have proportioned their works to approximate the golden ratio.
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