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EULER'S CONSTANT
(for NAPERIAN LOGARITHMS)

Mnemonics are often employed to memorise useful figures to several decimal places by constructing sentences that contain words of different lengths, each word-length representing each different digit.

Here's a mnemonic for Euler's constant (e), which is the base of Naperian (also Natural or Hyperbolic) logarithms. It identifies the constant to 10 decimal places:

" To express 'e', remember to memorise a sentence to simplify this! "

( ie. 2 . 7 1 8 2 8 1 8 2 8 4 )

The value of the constant is derived from a series which can be calculated infinitely:

e = 1 +[1/1] +[1/1*2] +[1/1*2*3] +[1/1*2*3*4]... to infinity

= 1 +1 +1/2 +1/6 +1/24 etc = 2.71828 (to 5 places)

John Napier invented logarithm tables in 1614 to aid the calculation of large numbers. They have a base e which is a different base to those of common logarithms (so called because they have a decimal base 10, the most common numerical system in use).

A logarithm is another word for power or index, and logarithms are used to simplify computations involving powers or indices, so that for example as 100 = 102, then 2 is called the common log of 100, or log10100=2. Where the power is not a whole number or the base is not 10 then logarithms become very useful as a means of expression and calculation (eg. log102=0.3010 and log216=4).

Although logs calculated to base 10 are usually employed for calculations, more advanced Mathematics and Engineering often require the more practical use of Napier's natural or hyperbolic logs instead.

Incidentally the constant sign e should not be confused with the exponent sign E used in algebraic operations generally. E is mostly used to express extremely large or small figures, eg. 314E-2 (=3.14) and 314E8 (=31,400,000,000).

 

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