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ArishMell · 70-79, M
Only 1 and 2, but I know of the uses for a few others.
Number 2, Napier's law of logarithms, is purely arithmetical, but part of a very powerful tool for easily solving awkward multiplication, division and power "sums". Although the calculator has displaced the log / antilog tables for arithmetic, logarithms are still important in many scientific laws. The most familiar perhaps is the deciBel, the logarithmic ratio used in measuring and calculating the intensities and powers of acoustic and electrical signals*.
Number 3 is part of the enormous field of Calculus used in so many Scientific and Engineering calculations.
Number 5 is used for solving problems involving square roots of negative values by what are called "Complex Numbers"; used for example in Vector calculations of a.c. electrical signals.
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Most of the rest are parts of particular scientific areas - and anyway I regret to say that they are beyond any maths alone I could have ever learnt! Indeed, for most of those equations you need understand both mathematics and those specific fields to considerable depth.
Consequently most of them don't "do" anything on their own.
Number 1, Pythagoras' Theorem, only means anything as the proportions of a right-angled triangle. Standing alone, it is self-evident but lacks identity or purpose, because any number can be described by the sum of two squares, and any number has a square root.
Number 13, Einstein's equation so often quoted without any context, is not explicable without explaining the General Theory of Relativity, and the relationship the formula describes.
I don't know Fourier's original line of study but a mathematical tool called the Fast Fourier Transform is used in analysing the frequencies mixed up in complicated spectra.
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*(The deciBel and Bel are not single, linear units like the metre and gramme. Quoting a sound pressure-level as of [i]x[/i] dB, is shorthand within its understood context, for an otherwise rather unwieldy description.
For measuring sound in air, the full form is "[i]x[/i]dB referred to 20µPa". That 20 micro-Pascals is the faintest detectable by the fully-healthy human ear, so gives 0dB as the reference-level [i]but only for that purpose[/i]. Since the Bar (standard atmospheric pressure) = 100 000 000 000µPa, that shows just how staggeringly sensitive is the ear. )
Marine acoustics uses 1µPa for its 0dB reference.
Neither scale can use 0 micro-Pascals as its reference because that would give the arithmetically-impossible division by 0 in the conversion to deciBels . )
Number 2, Napier's law of logarithms, is purely arithmetical, but part of a very powerful tool for easily solving awkward multiplication, division and power "sums". Although the calculator has displaced the log / antilog tables for arithmetic, logarithms are still important in many scientific laws. The most familiar perhaps is the deciBel, the logarithmic ratio used in measuring and calculating the intensities and powers of acoustic and electrical signals*.
Number 3 is part of the enormous field of Calculus used in so many Scientific and Engineering calculations.
Number 5 is used for solving problems involving square roots of negative values by what are called "Complex Numbers"; used for example in Vector calculations of a.c. electrical signals.
.
Most of the rest are parts of particular scientific areas - and anyway I regret to say that they are beyond any maths alone I could have ever learnt! Indeed, for most of those equations you need understand both mathematics and those specific fields to considerable depth.
Consequently most of them don't "do" anything on their own.
Number 1, Pythagoras' Theorem, only means anything as the proportions of a right-angled triangle. Standing alone, it is self-evident but lacks identity or purpose, because any number can be described by the sum of two squares, and any number has a square root.
Number 13, Einstein's equation so often quoted without any context, is not explicable without explaining the General Theory of Relativity, and the relationship the formula describes.
I don't know Fourier's original line of study but a mathematical tool called the Fast Fourier Transform is used in analysing the frequencies mixed up in complicated spectra.
' ' '
*(The deciBel and Bel are not single, linear units like the metre and gramme. Quoting a sound pressure-level as of [i]x[/i] dB, is shorthand within its understood context, for an otherwise rather unwieldy description.
For measuring sound in air, the full form is "[i]x[/i]dB referred to 20µPa". That 20 micro-Pascals is the faintest detectable by the fully-healthy human ear, so gives 0dB as the reference-level [i]but only for that purpose[/i]. Since the Bar (standard atmospheric pressure) = 100 000 000 000µPa, that shows just how staggeringly sensitive is the ear. )
Marine acoustics uses 1µPa for its 0dB reference.
Neither scale can use 0 micro-Pascals as its reference because that would give the arithmetically-impossible division by 0 in the conversion to deciBels . )