File:01-Würfelverdoppelung-E-15-Animation.gif
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Summary
[edit]| Description |
Deutsch: Würfelverdoppelung, Näherungskonstruktion als Animation
English: Doubling the cube, proximity construction as animation |
| Date | |
| Source | Own work |
| Author | Petrus3743 |
| Other versions |
 Doubling the cube, approximate construction  Doubling the cube, final image for the proximity construction  Verdoppelung des Würfels als Animation |
Ergebnis
[edit]Bezogen auf einem Würfel mit der Seitenlänge a1 = 1 [LE]
[edit]- Konstruierte Seitenlänge des verdoppelten Würfels in GeoGebra
- Seitenlänge des verdoppelten Würfels
- Absoluter Fehler der konstruierten Seitenlänge des verdoppelten Würfels
- Volumen des verdoppelten Würfels mit konstruierter Seitenlänge in GeoGebra
- Volumen des verdoppelten Würfels
- Absoluter Fehler des Volumens mit konstruierter Seitenlänge
![{\displaystyle a_{2}=1{,}259921049894873...\;[LE]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/041a4059a1fc1f8352319380670455ac8496b8ee)
![{\displaystyle a_{2\;SOLL}={\sqrt[{3}]{2}}=1{,}259921049894873164...\;[LE]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/73d15cde9fb81b8ad14681250e36b6bf546e97ea)
![{\displaystyle Fa_{2}=-1{,}64...E-16\;[LE]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/83b0ac28c8876664c03d1e8b8703e50821714990)
![{\displaystyle a_{2}{^{3}}=1{,}999999999999999215...\;[VE]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fa8d739a2e0025c1fca1ca28921adedaff307edc)
![{\displaystyle a_{2\;SOLL}{^{3}}=2{,}0\;[VE]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/72752c32a8596f64aec9391ebe0219a29e14e6a1)
![{\displaystyle F_{V}=a_{2}{^{3}}-a_{2\;SOLL}{^{3}}=-7{,}84...E-16\;[VE]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2cb075b6da4d1ea8cc817836fd2ba55acd335bb2)
Beispiel um den Fehler zu verdeutlichen
[edit]- Bei einem Würfel 1 mit der Seitenlänge a1 = 1 Mrd. km (das Licht bräuchte für diese Strecke ca. 55 min) wäre der Fehler der konstruierten Seitenlänge a2 des verdoppelten Würfels 2 ca. 0,2 mm.
- Bei einem Würfel 1 mit der Seitenlänge a1 = 10 km wäre der Fehler des Volumens vom verdoppelten Würfels 2 ca. 0,8 dm3 oder ca. 1 Liter.
Score
[edit]In relation to a cube with side length a1 = 1 [unit of length]
[edit]- Constructed side length of the doubled cube in GeoGebra
- Side length of the doubled cube
- Absolute error of the constructed side length of the doubled cube
- Volume of the doubled cube with a constructed side length in GeoGebra
- Volume of the doubled cube
- Absolute error of the volume with a constructed side length
![{\displaystyle a_{2}=1.259921049894873...\;[unit\;of\;length]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8a8e7a5de33ed846905bb4134b58f4ed9bd87bc1)
![{\displaystyle a_{2\;should}={\sqrt[{3}]{2}}=1.259921049894873...\;[unit\;of\;length]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1cf22e14fabb8ebc613c609a7e46da4a1c004769)
![{\displaystyle Fa_{2}=-1.64...E-16\;[unit\;of\;length]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/83cf665ee60399470d2642daa44c34fd613e3a50)
![{\displaystyle a_{2}{^{3}}=1.999999999999999215...\;[unit\;of\;length]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/59abb4e92e358dcd3d6d22058d553af217c6705a)
![{\displaystyle a_{2\;should}{^{3}}=2.0\;[unit\;of\;volume]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0412b495d0ecc4a5258e62e9a19ca7ffb77b8138)
![{\displaystyle F_{V}=a_{2}{^{3}}-a_{2\;should}{^{3}}=-7.84...E-16\;[unit\;of\;volume]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3f7df8fa01200de8d44240e4feae3240bd1d488d)
Example to illustrate the error
[edit]
- For a cube 1 with the side length a1 = 1 billion km (the light would need about 55 minutes for this distance), the error of the side length a2 of the doubled cube 2 would be approx. 0.2 mm.
- For a cube 1 with the side length a1 = 10 km, the error of the volume of the doubled cube 2 would be approx. 0.8 dm3 or approx. 1 liter.
Licensing
[edit]
I, the copyright holder of this work, hereby publish it under the following license:
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 15:41, 3 May 2018 | | 777 × 603 (92 KB) | Petrus3743 (talk | contribs) | eine Abstandsbezeichnung korr. |
| 16:52, 19 June 2016 |  | 685 × 609 (87 KB) | Petrus3743 (talk | contribs) | FI1ː Strecke in Abstand umgewandelt | |
| 15:08, 18 June 2016 |  | 685 × 609 (87 KB) | Petrus3743 (talk | contribs) | User created page with UploadWizard |
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