File:Complex Fourier series animation tracing the letter 'e'.webm
Jump to navigation
Jump to search
Size of this JPG preview of this WEBM file: 800 × 533 pixels. Other resolutions: 320 × 213 pixels | 640 × 427 pixels | 1,080 × 720 pixels.
Original file (WebM audio/video file, VP9/Opus, length 4 min 32 s, 1,080 × 720 pixels, 551 kbps overall, file size: 17.88 MB)
Captions
Captions
the front and back planes show the real and imaginary parts of the sum of the first +/-n terms of the complex Fourier series that has coefficients to converge to a tracing of the letter 'e' (for exponential)
Summary[edit]
| Description |
English: 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. |
| Date | |
| Source | Own work |
| Author | Greg Sepesi |
The Julia source code for generating the frames of the animation are in the appendix of the essay Zeno's Enduring Example at https://towardsdatascience.com/zenos-illustrative-example-bb371b99f25a?source=friends_link&sk=8a6f90c96adf5b4a28d223a4a0db7350
Licensing[edit]
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
 |
This file was uploaded as part of Wiki Science Competition 2021. |
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 17:07, 28 December 2021 | 4 min 32 s, 1,080 × 720 (17.88 MB) | Gj7 (talk | contribs) | Uploaded own work with UploadWizard |
You cannot overwrite this file.
File usage on Commons
The following page uses this file:
Transcode status
Update transcode statusFile usage on other wikis
The following other wikis use this file:
- Usage on en.wikipedia.org