File:0.999... = 1 CircleGraphProof.svg
Original file (SVG file, nominally 625 × 690 pixels, file size: 6 KB)
Captions
Summary[edit]
Description0.999... = 1 CircleGraphProof.svg |
English: A circle of unit area as geometric proof of the equality that 0.999…= 1. Explanation:
A circle of unit area can be sliced up in any way and all of its parts added together will always equal 1. This circle is sliced up into ever-thinner pie slices where the first slice leaves 90% untouched (0.9), the second slice leaves 90% of the remaining wedge untouched (0.09), the third slice leaves 90% of that remaining wedge untouched (0.009), and this process continues without end. The summation of all slices produces the infinite series: diagramBlue = RGBColor[0.4, 0.8, 1]; coord[n_Integer] := { Cos[(1/4 + 10^(-n)) 2 \[Pi]], Sin[(1/4 + 10^(-n)) 2 \[Pi]] } radius[n_Integer] := Line[{{0, 0}, coord[n]}] pointLabel[label_String, points_List : {x_, y_}] := Text[ TextCell[ label, "Text", CellFrame -> True, CellFrameMargins -> 0.1, CellFrameColor -> diagramBlue, Background -> White ], points ] diagram = Show[ Graphics[{ {diagramBlue, EdgeForm[Black], Disk[]}, radius[0], radius[1], radius[2], radius[3], pointLabel["0.9\n36°", coord[1] + {-0.05, 0.11}], pointLabel[ "0.09\n3.6°", {coord[2][[1]] - 0.05, coord[0][[2]] + 0.12}], pointLabel[ "0.009\n0.36°", {coord[3][[1]] + 0.05, coord[0][[2]] + 0.12}] }], ImageSize -> 500 ] Export[FileNameJoin[{Directory[], "Downloads", "0.999... = 1 CircleGraphProof.svg"}], diagram] |
Date | |
Source | Own work based on: 0.999... = 1 CircleGraphProof.png |
Author | CalendulaAsteraceae |
SVG development InfoField |
Licensing[edit]
- 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.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 20:29, 14 September 2023 | 625 × 690 (6 KB) | CalendulaAsteraceae (talk | contribs) | improve code | |
02:29, 17 March 2021 | 450 × 471 (27 KB) | CalendulaAsteraceae (talk | contribs) | Actually changed background | ||
02:28, 17 March 2021 | 450 × 471 (27 KB) | CalendulaAsteraceae (talk | contribs) | Added white background | ||
12:29, 16 March 2021 | 450 × 471 (27 KB) | CalendulaAsteraceae (talk | contribs) | Uploaded own work with UploadWizard |
You cannot overwrite this file.
File usage on Commons
The following 2 pages use this file:
File usage on other wikis
The following other wikis use this file:
- Usage on en.wikipedia.org
- Usage on fr.wikibooks.org
Metadata
This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.
Width | 500pt |
---|---|
Height | 552.286pt |