Metallic mean
The metallic means (also ratios or constants) of the successive natural numbers are the continued fractions: The golden ratio (1.618...) is the metallic mean between 1 and 2, while the silver ratio (2.414...) is the metallic mean between 2 and 3. The term "bronze ratio" (3.303...), or terms using other names of metals (such as copper or nickel), are occasionally used to name subsequent metallic means. The values of the first ten metallic means are shown at right. Notice that each metallic mean is a root of the simple quadratic equation:, where is any positive natural number.
Bronze Fibonacci numberBronze meanBronze ratioBronze rectangleBronze spiralBronze triangleCopper meanCopper meansCopper ratioGeneralizations of Fibonacci numbersGolden ratioList of numbersMetalic meansMetallic constantMetallic constantsMetallic meansMetallic ratioMetallic ratiosNickel meanNickel meansNickel ratioPisano periodPisot–Vijayaraghavan numberPlastic numberSilver meansSilver ratioVera W. de Spinadel
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Metallic mean
The metallic means (also ratios or constants) of the successive natural numbers are the continued fractions: The golden ratio (1.618...) is the metallic mean between 1 and 2, while the silver ratio (2.414...) is the metallic mean between 2 and 3. The term "bronze ratio" (3.303...), or terms using other names of metals (such as copper or nickel), are occasionally used to name subsequent metallic means. The values of the first ten metallic means are shown at right. Notice that each metallic mean is a root of the simple quadratic equation:, where is any positive natural number.
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The metallic means (also ratio ...... tios approach the bronze mean.
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Gold, silver, and bronze ratios within their respective rectangles.
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Golden ratio within the pentagram and silver ratio within the octagon.
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The metallic means (also ratio ...... s any positive natural number.
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Metallic mean
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