File:Central dilation.svg
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Size of this PNG preview of this SVG file: 340 × 185 pixels. Other resolutions: 320 × 174 pixels | 640 × 348 pixels | 1,024 × 557 pixels | 1,280 × 696 pixels | 2,560 × 1,393 pixels.
Original file (SVG file, nominally 340 × 185 pixels, file size: 4 KB)
Summary
| Description |
English: A given trapezoid A1B1B2A2 with bases (parallel sides) A1B1, A2B2 specifies a central dilation or homothecy of an affine space (mapping A1 on A2, B1 on B2), iff the other two sides A1A2, B1B2 are not parallel. In this case, the latter sides meet in a point Z, which is the center of the dilation. Given this center and a pair (B1, B2) of a point and its image, the image of an arbitrary point C1 not on the line B1B2 can be constructed as shown in the picture. Deutsch: Ein Trapez A1B1B2A2, in dem die Seiten A1B1, A2B2 parallel sind, bestimmt genau dann eine zentrale Dilatation, bei der A1 auf A2 und B1 auf B2 abgebildet wird, wenn die Seiten A1A2, B1B2 nicht parallel sind. Die letztgenannten Seiten (Verbindungsgeraden!) schneiden sich dann in einem Zentrum Z. Das Bild C2 eines beliebigen Punktes C1, der nicht auf der Geraden B1B2 liegt, kann dann wie in dem Bild gezeigt aus Z,B1,B2 konstruiert werden. |
| Date | |
| Source | Own work |
| Author | KlioKlein |
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 15:26, 13 February 2012 | | 340 × 185 (4 KB) | wikimediacommons>KlioKlein |
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