Calculation
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| Binary | 1.1001111000110111011... |
| Decimal | 1.6180339887498948482... |
| Hexadecimal | 1.9E3779B97F4A7C15F39... |
| Continued fraction | |
| Algebraic form | |
| Infinite series | |
Two quantities a and b are said to be in the golden ratio φ if:
One method for finding the value of φ is to start with the left fraction. Through simplifying the fraction and substituting in b/a = 1/φ,
it is shown that
Multiplying by φ gives
which can be rearranged to
Using the quadratic formula, the only positive solution is
Read more about this topic: Golden Ratio
Famous quotes containing the word calculation:
“Common sense is the measure of the possible; it is composed of experience and prevision; it is calculation appled to life.”
—Henri-Frédéric Amiel (1821–1881)
““To my thinking” boomed the Professor, begging the question as usual, “the greatest triumph of the human mind was the calculation of Neptune from the observed vagaries of the orbit of Uranus.”
“And yours,” said the P.B.”
—Samuel Beckett (1906–1989)