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# Definition and uses of the number e in Mathematics

Also called “Napier’s constant,” the number e serves as the basis for the logarithmic calculation. It is an irrational number that is written to an infinite number of decimal places without a logical sequence. That is, a number that cannot be counted?

### History of the number e : Definition and uses of the number e in Mathematics

Unlike rational numbers, whose decimal development is called periodic, the number e has an infinity of decimal places without logical order.

The relation 2/7, for example, is equal to 0.285714285714285714 … The decimals that appear after the comma show the recurring sequence 285714 played to infinity.

Today, we know that e = 2.71828182845904523536028747135266249775724709369995957 … and that  there are more than 8 billion possible decimal places.

On January 3, 2019, mathematician Gerald Hofmann succeeded in proving the existence of 8 trillion decimal places after the decimal point, beating the previous record of 5 trillion decimal places found in 2016.

In 1614, John Napier publishes  Mirifici logarithmorum canonis descriptio , a work on arithmetic that presents the creation of the logarithm, a tool to simplify trigonometric calculations used for astronomy.

Although our calculator and computers give the value of algorithmic calculation in one click and today all math teachers can teach the logarithmic function to their students, this was not the case in modern times.

The works of J. Napier consisted of being able to add instead of multiplying, subtract instead of dividing and divide by 2 instead of taking a square root; that’s the purpose of the logarithm.

At the beginning, the logarithmic tables had 8 decimal places. If 10 3  = 10 x 10 x 10 = 1000, then log (1000) = 3 and if 10 x  = y then log (y) = x.

Ok, but what is the relationship with the number e? Well, it  allows us to determine for what value the natural logarithm, ln (x), is equal to 1 .

The number e has 400 years of history in mathematics. The mathematician Jacques Bernoulli (1654-1705), the inventor of the famous eponymous probability law, seeks to maximize a goldsmith’s profits using compound interest.

You discover that the interest calculated in a year is less than if it is estimated monthly, and even less when it is calculated daily. Thanks to a commercial demonstration, he discovered the number e.

Later, the Swiss  Leonhard Euler (1707-1783) theorized  the number  e,  as an expression of the exponential function , using continuous fraction expansion.

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