File:Archimedes Parabola.svg

From Wikimedia Commons, the free media repository

Jump to: navigation, search

Archimedes_Parabola.svg(SVG file, nominally 474 × 419 pixels, file size: 8 KB)

Description
English: Archimedean decomposition of a parabolic segment into infinitely many triangles. Each green triangle is 1/8 of the area of the blue triangle, each yellow triangle is 1/8 the area of a green triangle, and so forth.

Assuming the blue triangle has area 1, the total area under the parabola is

1 \,+\, \frac{2}{8} \,+\, \frac{4}{64} \,+\, \cdots
=1 \,+\, \frac{1}{4} \,+\, \frac{1}{16} \,+\, \cdots.
The sum of this en:geometric series is 4/3.
Date

unknown/2009-02-03

Source

en:File:Archimedes_Parabola.png

Author

en:User:Jim.belk,uploader

Permission
(Reusing this image)
Public domain I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide.

In case this is not legally possible:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.


Afrikaans | Alemannisch | Aragonés | العربية | Asturianu | Azərbaycan | Беларуская (тарашкевіца) | Български | Català | Cebuano | Soranî / کوردی | Česky | Cymraeg | Dansk | Deutsch | Ελληνικά | English | Esperanto | Español | Eesti | Euskara | Estremeñu | فارسی | Suomi | Français | Galego | עברית | हिन्दी | Hrvatski | Magyar | Հայերեն | Bahasa Indonesia | Ido | Íslenska | Italiano | 日本語 | ქართული | ភាសាខ្មែរ | 한국어 | Ripoarisch | Kurdî / كوردی | Latina | Lietuvių | Latviešu | 文言 | Македонски | Bahasa Melayu | Plattdüütsch | Nederlands | ‪Norsk (nynorsk)‬ | ‪Norsk (bokmål)‬ | Polski | Português | Română | Русский | Slovenčina | Slovenščina | Shqip | Српски / Srpski | Svenska | ไทย | Tagalog | Türkçe | Українська | Vèneto | Tiếng Việt | Walon | 吴语 | 中文 | ‪中文(简体)‬ | ‪中文(繁體)‬ | 粵語 | +/−

svg version of the image from en.

File history

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

Date/TimeThumbnailDimensionsUserComment
current18:25, 3 February 2009Thumbnail for version as of 18:25, 3 February 2009474×419 (8 KB)Ghazer (talk | contribs) ({{Information |Description={{en|1=Archimedean decomposition of a parabolic segment into infinitely many triangles. Each green triangle is 1/8 of the area of the blue triangle, each yellow triangle is 1/8 the area of a green triangle, and so forth. Assum)

There are no pages that link to this file.