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### Page 1143 of Mathematical Reviews Vol. , Issue 86c [page]

1986 Mathematical Reviews
It is called a generalized elation if C lies on |, otherwise a generalized homology. The authors classify generalized homologies of Desarguesian planes.  ...  The author notes that in Theorem 1 the prime p must be greater than 3 (as already stated in the original review). Dempwolff, U. (D-KSRL) A note on the Figueroa planes. Arch. Math.  ...

### Nine lines are needed to avoid any three general points

Roy Mikael Skjelnes
2018 The Mathematics Enthusiast
We construct nine lines in the plane over the integers having the property that for any three general points in the plane over any field, at last one of the constructed lines avoids the three points.  ...  Clearly, if one has seven general lines in the projective plane over a field, then at least one of the lines will avoid any given three points defined over that field.  ...  And, if F = F 2 then the nine lines of L specializes to the seven lines of the Fano plane, where we already have noted that at least one line avoids a given three general points.  ...

### On projections of ruled and veronese surfaces

E Ballico, Ph Ellia
1989 Journal of Algebra
Note that up to a projective transformation, there is a unique W(d) spanning P(d): use induction on the number of planes in W(d).  ...  on d, k, a general projection T of X(n) into Pk has maximal rank.  ...

### Thrackles: An Improved Upper Bound [chapter]

2018 Lecture Notes in Computer Science
Generalized Thrackle An embedding of a graph G in the projective plane is a parity embedding if every odd cycle of G is one-sided and every even cycle of G is two-sided.  ...  Generalized Thrackle An embedding of a graph G in the projective plane is a parity embedding if every odd cycle of G is one-sided and every even cycle of G is two-sided.  ...  Any quasi-thrackle on n vertices has at most 3  ...

### Page 515 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 4, Issue [page]

1898 American Mathematical Society. Bulletin of the American Mathematical Society
Miller: Comptes Rendus, vol. 126 (1898), pp. 1406-1408. t¢ In a note on the general projective transformation, Annals of Mathe- matics, vol. 10, No. 1, the forms of the finite projective transformations  ...  Geometrically, infinitesimal projective transformations of space are those infinitesimal point transformations which transform a plane into a plane,7 e., which leave invariant the family of «* planes of  ...

### 159. A Note on the Gnomonic Projection

Harold Hilton
1904 Mathematical Gazette
Note 157). HAROLD HILTON. 159. [P. 3. b. ca.] A note on the gnomonic projection.  ...  Note 157). HAROLD HILTON. 159. [P. 3. b. ca.] A note on the gnomonic projection.  ...

### Surviving Dominant Planes in Uncalibrated Structure and Motion Recovery [chapter]

Marc Pollefeys, Frank Verbiest, Luc Van Gool
2002 Lecture Notes in Computer Science
Traditional approaches fail when the features common to three consecutive views are all located on a plane. This is, however, a situation that is often hard to avoid in man-made environments.  ...  a common plane and poses of cameras only seeing planar features) till after self-calibration.  ...  Note, however, that these techniques require multiple planes or general structure and would therefore fail on the cases treated by this paper.  ...

### Page 53 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 27, Issue [page]

1920 American Mathematical Society. Bulletin of the American Mathematical Society
In the first place it is proved that every cyclide may be generated in an infinite number of ways by two projective pencils of spheres (of which one may degenerate into a pencil of planes).  ...  It also leads to a generalized cyclide which may be called a quintic cyclide, whose definition is contained in the following theorem: The tangent planes of a quadric cone and an independent projective  ...

### Radii of the E8 Gosset Circles as the Mass Excitations in the Ising Model [article]

Mehmet Koca, Nazife Ozdes Koca
2012 arXiv   pre-print
A special non-orthogonal projection of the simple roots on the Coxeter plane leads to exactly the numerical values of the masses of the bound states as 0.4745, 0.7678, 0.9438, 1.141, 1.403, 1.527, 1.846  ...  These masses turn out to be proportional to the radii of the Gosset's circles on the Coxeter plane obtained by an orthogonal projection of the root system of E8 .  ...  are mapped on the Coxeter plane by using the orthogonal projection.  ...

### Elation Laguerre planes of order 16 are ovoidal

Günter F. Steinke
2006 Journal of combinatorial designs (Print)
We conduct a computer search for elation Laguerre planes of order 16 and show that each such plane is ovoidal.  ...  The search results also confirm the numbers of hyperovals through certain points in the dual translation planes of order 16 given in [15] . MSC 2000: 51E25, 51B15.  ...  This planar description of a Laguerre plane must then be extended by the points of one generator where one has to adjoin a new point to each line and to each oval of the projective plane as above.  ...

### Page 26 of The American Mathematical Monthly Vol. 35, Issue 1 [page]

1928 The American Mathematical Monthly
26 NOTE ON STEREOGRAPHIC PROJECTION |Jan., Any circle on the sphere is cut out by a plane, », which we assume does not pass through P.  ...  Since all plane sections of a sphere are circles, we see that any circle on > is the projection of a circle on the sphere.  ...

### Page 2 of Annals of Mathematics Vol. 9, Issue 1 [page]

1894 Annals of Mathematics
Consider a prismoid, project it orthogonally on a plane parallel to the bases.  ...  Let /’ be the projection on the line 2,2, of the point in which the generator pierces any such third plane.  ...

### A note on the group of projectivities of finite planes

Peter Müller, Gábor Nagy
2008 Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial
In this short note we show that the group of projectivities of a projective plane of order 23 cannot be isomorphic to the Mathieu group M 24 . By a result of T.  ...  Grundhöfer [6] , this implies that the group of projectivities of a non-desarguesian projective plane of finite order n is isomorphic either to the alternating group A n+1 or to the symmetric group S n  ...  Introduction Any projective plane Π can be coordinatized by a planar ternary ring (R, T ), see [7] .  ...

### A QUADRATIC MAPPING IN PROJECTIVE FOUR-DIMENSIONAL SPACE

Oeme Bottema
1979 Demonstratio Mathematica
It is shown that through a point A of P^ passes, in general, one projecting plane 9(A). A projection plane ir is introduced, not passing through T, and intersecting r1 at T^' (i=1,2).  ...  In projective 4 -space P^ two planes t^ and r^ are given, intersecting at the point T. A projecting plane 9 is defined as a plane through T intersecting both r^ and z^ in a straight line.  ...  It is shown that through a point A of P^ passes, in general, one projecting plane 9(A). A projection plane ir is introduced, not passing through T, and intersecting r1 at T^' (i=1,2).  ...

### 158. On a Theorem in Inversion

Harold Hilton
1904 Mathematical Gazette
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive.  ...  Note 157). HAROLD HILTON. 159. [P. 3. b. ca.] A note on the gnomonic projection.  ...  Note 157). HAROLD HILTON. 159. [P. 3. b. ca.] A note on the gnomonic projection.  ...
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