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Euler's Number (e):
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Euler's number (e ≈ 2.71828) is a mathematical constant that is the base of the natural logarithm. It is one of the most important numbers in mathematics, particularly in calculus and complex analysis.
Key mathematical properties:
Explanation: e is unique in that the function e^x is its own derivative and integral, making it fundamental in differential equations and exponential growth models.
Details: e appears in compound interest calculations, population growth models, radioactive decay, probability theory, and many areas of physics and engineering.
Tips: Enter any numerical value and select an operation (multiply by e, divide by e, or raise to power e) to perform calculations involving Euler's number.
Q1: Why is e called Euler's number?
A: It is named after the Swiss mathematician Leonhard Euler, who introduced and popularized many of its properties in the 18th century.
Q2: How is e different from π?
A: While π (3.14159) relates to circles and geometry, e (2.71828) relates to exponential growth and calculus. Both are transcendental numbers.
Q3: What is the natural logarithm?
A: The natural logarithm (ln) is the logarithm to the base e. It is the inverse function of the exponential function e^x.
Q4: Where does e appear in real life?
A: e appears in compound interest calculations, population growth models, radioactive decay, and many natural phenomena that follow exponential patterns.
Q5: Is e a rational number?
A: No, e is an irrational number (cannot be expressed as a simple fraction) and is also transcendental (not a root of any non-zero polynomial equation with rational coefficients).