The Number Known as e.

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Presentation transcript:

The Number Known as e

Where does it come from? The first references to it were in Napier’s natural logarithms although no mention was made of the constant itself The discovery is credited to Jacob Bernoulli who attempted to find the value of: Leonhard Paul Euler started to use the letter e for the constant in 1727. Why the letter ‘e’ – nobody really knows. After that e crops up all over the place. e is irrational (not a ratio of integers) and transcendental (not the root of any non-zero polynomial with rational coefficients.

Here are some very interesting facts about e . . . The number e is the unique positive real number such that 2. The number e is the unique positive real number such that The following three characterizations can be proven equivalent: 3. The number e is the limit Similarly: 4. The number e is the sum of the infinite series where n! is the factorial of n. 5. The number e is the unique positive real number such that .