The article discusses the significance of the number e, approximately 2.71828, in exponential functions and logarithms. Despite seeming artificial in origin, e has special mathematical properties. It stemmed from efforts to simplify compound interest calculations and logarithmic tables in the 16th century. The number e is irrational, transcendental, and closely related to trigonometric functions, like pi. Its unique property lies in the slope of exponential functions and logarithms, where the base e ensures the curve intersects the line y=x+1 at a 45-degree angle. This characteristic of e influences various mathematical concepts and formulas, showcasing its importance in mathematics.
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