Central Collineations: Complete Quadrilateral, Involution, and Hexagon Theorems

2020 ◽  
pp. 87-97
Author(s):  
Christopher Baltus
Keyword(s):  
Central Collineations ◽  
Complete Quadrilateral

scholarly journals Proof of a Geometrical Theorem

1886 ◽  
Vol 5 ◽  
pp. 51-51
Author(s):  
W. J. Macdonald
Keyword(s):  
Complete Quadrilateral

The middle points of the diagonals of a complete quadrilateral are collinear.Let ABCDEF be a complete quadrilateral (see fig. 70), and X, Y, Z, the middle points of its diagonals. To prove X, Y, Z, collinear.

An S-Configuration in Euclidean and Elliptic n-space

1958 ◽  
Vol 10 ◽  
pp. 489-501 ◽  
Author(s):  
Ram Sahib Mandan
Keyword(s):  
Higher Dimensions ◽  
Complete Quadrilateral

“The remarkable analogies which exist between the complete quadrilateral and the desmic system of points suggest that it may be possible to extend the properties considered above to spaces of higher dimensions”, remarks Prof. N. A. Court at the end of his paper (2). Here is an attempt in that direction in Euclidean as well as in elliptic 4-space, suggesting extensions in higher spaces. The corresponding figure, called an S-configuration, is discussed.

1814.The complete quadrilateral

1945 ◽  
Vol 29 (284) ◽  
pp. 70-71
Author(s):  
H.N. Haskell
Keyword(s):  
Complete Quadrilateral

scholarly journals A homomorphism theorem for projective planes

1971 ◽  
Vol 4 (2) ◽  
pp. 155-158 ◽  
Author(s):  
Don Row
Keyword(s):  
Projective Plane ◽  
Homomorphic Image ◽  
Inverse Image ◽  
Projective Planes ◽  
Homomorphism Theorem ◽  
Central Collineations

We prove that a non-degenerate homomorphic image of a projective plane is determined to within isomorphism by the inverse image of any one point. An application gives conditions for the preservation of central collineations by a homomorphism.

Some Elementary Projective Properties of the Four-Bar Linkage

1973 ◽  
Vol 95 (3) ◽  
pp. 721-724
Author(s):  
J. S. Marquez ◽  
D. P. Adams
Keyword(s):  
Practical Application ◽  
Connecting Rod ◽  
Complete Quadrilateral ◽  
Four Bar Linkage

The four-bar linkage defines a complete quadrilateral—a figure with extensive elementary projective properties. The undertaking is to search out and discover evidences or indicia of projective interrelationships in the geometry of the four-bar, such as concurrencies of lines, collineations of points, constancies of cross-ratios, harmonic divisions, tangencies of lines and curves, and others, toward the practical application of such properties in four-bar motion. Several of these have indeed been discovered and proved, each worth-while in its own right and each expressible as an instantaneous projective relationship between members of a simply-defined family of linkages. The most startling and applicable of the properties is the collineation of the centers of the inflection circles of the connecting-rod motions of the defined family.

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