# Trigonometry/The Gibbs Overshoot

From Wikibooks, open books for an open world

On the previous page, it can be seen that the approximations to the square wave go slightly above the wave, and then come down again. As more terms are added, this overshoot gets slightly greater but persists for a smaller range of values of x before dropping back to the right level. In the limit, as the number of terms tends to infinity, the maximum value reaches about 9% more than the level of the square wave. The precise value is

This overshoot is known as the **Gibbs effect**, **Gibbs phenomenon** or **Gibbs overshoot**, after the mathematical physicist Josiah Gibbs (1839-1903), who explained the phenomenon in 1899.

This page or section is an undeveloped draft or outline.You can help to develop the work, or you can ask for assistance in the project room. |