Projective planes

(P is at the intersection of BD and CE; Q and R are defined similarly.) The second is Desargues' Theorem, that is, if the two triangles ABC and A1, B1 C1 are in perspective from O, then PQR are collinear. [...]on your copy of figure 2, label OAA v OBB r OCC ^ with three triples of collinear num...

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Bibliographic Details
Published in:Mathematics Teaching 2018-12 (264), p.17-19
Main Author: Burn, Bob
Format: Article
Language:English
Subjects:
Geometric Concepts
Geometry
Infinity
Mathematics Instruction
Numbers
Planes
Online Access:Get full text
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Summary:(P is at the intersection of BD and CE; Q and R are defined similarly.) The second is Desargues' Theorem, that is, if the two triangles ABC and A1, B1 C1 are in perspective from O, then PQR are collinear. [...]on your copy of figure 2, label OAA v OBB r OCC ^ with three triples of collinear numbers from the 4 x 13 array, and from the array work out the corresponding numbers for PQR, and check that they are collinear. Removing the line at infinity You may ask, "What has happened to the line at infinity" in the seven-point and thirteen-point planes. Because of the cyclic display of their points and lines, just which line was the line at infinity is no longer detectable in these two projective planes.
ISSN:0025-5785