# Complex Fourier series animation tracing the letter 'e'

The animation gives four perspectives of a converging complex Fourier series as more terms are added. 1) The front plane shows a two arm aggregation of series terms where one arm is the sum of the positive rotating terms and the other arm is the sum of the negative rotating terms. 2) The back plane shows a one arm zigzag aggregation of series terms where positive and negative rotating terms are added as pairs producing the zigzag appearance. 3) The intermediate planes (trapezoid baseline) show the frequency and phase information as rotating trapezoids representing individually scaled and rotating terms of the complex geometric series. 4) The audio is what those rotating trapezoids would sound like if they were rotating 3530 times faster.

- Kind: Cartoon
- Year: 2021
- Runtime: 4 min
- By: Greg Sepesi
- Genres: Animation, Education, Science
- Archive: [Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Complex_Fourier_series_animation_tracing_the_letter_%27e%27.webm)
- Licence or status: [CC BY 4.0](https://creativecommons.org/licenses/by/4.0) (as the archive states it)
- Credit: Greg Sepesi
- Who can watch: Kids profiles and older (the archive gives no rating; placed by Invisible Network from its collection and subjects)

[Watch now](https://invisiblenetwork.ai/watch/archive/commons/113750584?play=1)