 |
|
| A B C D E F G H I J K L M N O P Q R S T U V W X Y Z |
| • HOME • ABOUT • CATEGORIES • USE OF TEXT AND IMAGES • NEWSLETTER   
|
Weierstrass' nondifferentiable function
The 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 CURVESAlso on this site:
Encyclopedia of Alternative Energy & Sustainable Living
Encyclopedia of History