## Weierstrass' nondifferentiable functionThe earliest known example of a pathological function –
a function that gives rise to a pathological
curve. It was investigated by Karl Weierstrass,
but had been first discovered by Bernhard Riemann,
and is defined as:where 0 < a < 1, b is a positive odd integer, and ab >
1 + 3π/2.The Weierstrass function is everywhere continuous but nowhere differentiable; in other words, no tangent exists to its curve at any point. Constructed from an infinite sum of trigonometric functions, it is the densely-nested oscillating structure that makes the definition of a tangent line impossible. ## Related category• FRACTALS AND PATHOLOGICAL CURVES | |||||

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