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The number e is another interesting number used in many areas of mathematics. If you want to learn about other interesting numbers, such as Pi and Phi, click here.

The number e came into mathematics in 1816 in Napier's work on logarithms. Logarithm as a word comes from two words - logos (word, account) and ariqmos (number).

Many people have contributed to the definition and explanation of the number e. The number itself is related to many concepts in mathematics.

In 1661 Huygens understood the relation between the rectangular hyperbola and logarithms. He examined the area under the rectangular hyperbola yx=1 and the logarithm. The fascinating fact is that the area under the rectangular hyperbola from 1 to e is equal to 1. Huygens also defined a curve which he called 'logarithmic' but in our terminology we would refer to it as an exponential curve, as its form is

Few decades later, in 1683 Jacob Bernoulli was examining the compound interest. He was trying to find the

He used the binomial theorem to show that the value of this limit has to lie somewhere between 2 and 3. We now know that this was the first approximation to e. It may be that Jacob Bernoulli was the first person to understand that the logarithmic is inverse of exponential function.

e appears in its own right for the first time in 1690 as a concept, but not yet as a letter 'e'. Leibniz then wrote a letter to Huygens in which he defined e, but used a letter b to denote it.

Euler then used the letter e to describe the same concept, in a letter to Goldbach in 1731. Euler made various discoveries relating to e, for example showing that

Euler gave the approximation of e=2.7182181828459045235.

Other interesting facts about e are that it is an irrational number - Euler did not explicitly prove this, but he gave the patterns which e satisfies, which led many mathematicians after him to say that in fact this was a proof. In fact, proof that e is irrational was given by Hermite in 1873.

Because e is irrational it doesn't end and it can't be written as a finite fraction. Click here to see e expressed as continued fraction or click here to download e to 10 000 places.

 

   

See more on the number e by clicking here.

Click on the picture below to find about Euler, who did a lot of work on e.

See more on other famous numbers by clicking here.

 

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