File:151221-Rectangular-model-of-Fano-plane.png
151221-Rectangular-model-of-Fano-plane.png (300 × 333 pixels, file size: 15 KB, MIME type: image/png)
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Summary
[edit]Description151221-Rectangular-model-of-Fano-plane.png |
English: Rectangular model of Fano plane
This rectangular model of PG(2,2), the projective plane over the 2-element Galois field GF(2), is related to the Miracle Octad Generator of R. T. Curtis. The black squares in each picture depict a two-dimensional vector subspace (plane) within the vector 3-space over GF(2). A vector 3-space over GF(2) becomes a projective 2-space when the origin of the space is deleted. In the resulting projective 2-space, vector-space planes through the origin become projective lines, with 3 rather than 4 points because the origin has been deleted. In the above image, the origin (top left subsquare) is retained, for the sake of visual symmetry. For details of the underlying geometry, see (for instance) Geometry and Symmetry by Paul B. Yale. |
Date | |
Source | Own work |
Author | Steven H. Cullinane |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 02:03, 22 December 2015 | 300 × 333 (15 KB) | Cullinane (talk | contribs) | User created page with UploadWizard |
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Horizontal resolution | 47.24 dpc |
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Vertical resolution | 47.24 dpc |