The main purpose of this page is to help you locate key definitions and concepts that are used in this site. For more complete defintions, see the references.

A.

• Absolute line. 35,
• Absolute point. 35,
• Abstract plane configuration. 2,
• Affine geometry. 19,
• Affine plane. 2, 2, 16, 16, 16, 16, 18, 18, 22, 28, 28,
• Affine plane, coordinate. 26,
• Affine plane, Desarguesian. 26,
• Affine plane, smallest. 22,
• Affine space. 35,
• Angle bisectors. 17,
• Antipodal points. 15,
• Axial collineation. 25,
• Automorphism. 6, 13a, 25,
• Automorphism, non-fixed point. 32,
• Automorphism group. 28,
• Axioms. 1, 34,
• Axis. 25,

B.

• Basis. 11,
• Bipartite. 29,
• Biplane. 2,
• Block. 31,

C.

• (c,l) - collineation. 25, 27,
• (c,l) - elation. 27,
• (c,l) - transitive. 25,
• Cartesian coordinates. 20,
• Central collineation. 25,
• Central collineations, complete set of. 25,
• Central projection. 19,
• Chromatic number. 30, 30,
• Circle at infinity. 17,
• Circuit. 33,
• Closure of a subset. 11,
• Collineations. 13a, 20, 25,
• Coloring. 30,
• Coloring, good. 30, 36,
• Complete set of central collineations. 25,
• Configuration. 28,
• Congruent. 0, 17,
• Conic, nondegenerate section. 35,
• Connected. 29,
• Connected components. 29,
• Consistent axiom system. 1,
• Cross product. 20,
• Cross ratio. 19,
• Cube geometry. 34,
• Cycle. 29,

D.

• de Bruijn-Erdos theorem. 9, 10, 32,
• Degree. 29,
• Degree sequence. 29,
• Degrees, sum of. 29,
• Dependant axiom system. 2,
• Derived geometry. 9,
• Desargues' configuration. 26, 27, 28,
• Desargues' Theorem. 24, 26,
• Desargues' Theorem (I). 24,
• Desargues' Theorem (II). 24,
• Desarguesian plane. 26, 27,
• Desarguesian plane, finite. 32, 33,
• Desarguesian planes, difference sets. 32,
• Design. 2, 16, 31,
• Difference set of order n. 32,
• Dihedral group. 28,
• Dimension. 11,
• Direct sum. 35,
• Doily. 33, 36,
• Dot product. 20,
• Duad. 36,
• Dual geometry. 4, 36,
• Duality. 15, 19, 20, 25, 27,

E.

• Edge. 29,
• Edges, multiple. 29,
• Elation. 25,
• Embedding. 18,
• Euclidean plane. 22, 26,
• Euclid's postulates. 22,
• Eulerian circuit. 33,
• Eulerian graph. 33,
• Exchange property. 12,

F.

• Fano plane. 2, 14, 16, 21, 25, 25, 28, 28, 31, 32, 32, 33,
• Field. 21,
• Finite affine plane. 22,
• Finite geometry. 1,
• Flag. 34,
• Flag, maximal. 34,
• Four Color Theorem. 30,

G.

• Generalized hexagon. 33,
• Generalized polygon. 20,
• Generalized Quadrangle. 2, 33, 36,
• Generating set. 11, 11,
• Generator-only diagram. 28,
• Generator-only graph. 31,
• Geometry.0, 1, 29, 34,
• Geometry, finite. 34,
• Geometry, infinite. 34,
• Graph. 5, 29,
• Graph, bipartite. 30,
• Graph, complement. 29,
• Graph, complete. 29, 29, 30, 31,
• Graph, complete bipartite. 36,
• Graph, isomorphism. 29,
• Graph, nonplanar. 30,
• Graph, planar. 30,
• Graph, real. 29,
• Graph, simple. 29,
• Grid. 36,
• Grid, square. 36,
• Group. 6,
• Great circle. 15,
• Group of automorphisms. 13a,

H.

• Hamiltonian. 33,
• Homogeneous coordinates. 20,
• Homogeneous equations. 20,
• Homogeneous geometry. 6, 9, 25, 28,
• Homology. 25, 27,
• Hyperbolic plane. 16, 16, 16,
• Hyperplane. 12,
• Hyperspace. 7,

I.

• Icosahedron. 36,
• Identity automorphism. 6, 6, 6, 25,
• Incidence. 0, 2,
• Incidence graph. 32, 33,
• Incidence matrix. 3,
• Incidence relation. 34,
• Incidence structure. 32,
• Inconsistent axiom system. 1,
• Independant axiom system. 2,
• Inconsistent equations. 20,
• Infinite affine plane. 22,
• Infinite geometry. 1,
• Inner product. 20,
• Invariant. 0,
• Isometry group. 28,
• Isomorphic. 6, 13a,
• Isomorphism. 6, 13a, 25, 29,

J.

K.

• Kirkman's School Girl Problem. 31,
• Kleins Erlanger Program. 0,

L.

• Line. 0, 1, 31, 34,
• Line at infinity. 14, 18, 19, 20, 27,
• Line regular. 9, 10,
• Linear map. 13a, 18,
• Linear map, image of. 13b,
• Linear space. 2, 8, 12, 12, 16, 32,
• Linearly independent. 11,
• Loop. 29,

M.

• Medians. 17,
• Model. 34,
• Moulton plane. 26,

N.

• Near-pencil. 9, 32,
• Near linear space. 1, 8, 18,
• Non-Euclidean geometry. 0,

O.

• Orbit. 32,
• Order. 2, 6, 10, 10, 16, 28, 31, 33, 36,
• Oval. 35,
• Ovoid. 35, 36,

P.

• p-gon geometry. 28,
• p_n configuration. 28,
• Pappian configuration. 27,
• Pappus. 23,
• Pappus' configuration. 28,
• Pappus' Theorem. 23,
• Parallel. 0,
• Parallel class. 16,
• Parameter. 36,
• Path. 29,
• Plane configuration. 20,
• Parallel lines. 16,
• Parallel postulate. 27,
• Parallel projection. 19,
• Parallelism. 26,
• Perspectivity. 25,
• Plane configuration. 2,
• Poincare disk model. 17,
• Point. 0,
• Point at infinity. 18, 19, 27,
• Point regular. 9, 10,
• Polar space. 35,
• Polar space, degenerate. 35,
• Polarities. 4,
• Polarity. 35,
• Projective coordinate plane. 21,
• Projective extension. 16,
• Projective geometry. 19,
• Projective line set. 20,
• Projective plane. 2, 2, 10, 12, 14, 15, 16, 16, 16, 18, 18, 19, 21, 25, 25, 28, 32,
• Projective plane, Desargues' Theorem. 27,
• Projective plane, Desarguesian. 27, 27, 27,
• Projective plane, incidence graph of. 33,
• Projective plane, Pappian. 27,
• Projective plane, Pappus' Theorem. 27,
• Projective plane, Desarguesian. 27,
• Projective plane, difference sets. 32,
• Projective property. 19,
• Projective space. 12, 16, 35,
• Proper subspace. 7,
• Punctured Fano plane. 9,

Q.

R.

• Rank. 34,
• Rational coordinate plane. 22, 22, 26,
• Real affine plane. 22, 34,
• Real coordinate plane. 22, 26,
• Real projective plane. 15, 17, 20, 22,
• Restricted geoemtry. 9,

S.

• Self dual. 20, 36,
• Singer cycle. 32,
• Singer's Theorem. 32, 33,
• Span. 11,
• Spread. 35, 36,
• Steiner Triple System (STS). 31,
• Straight line models. 28,
• Sub-geometry. 7,
• Subspace. 7,
• Syntheme. 36,
• Syntheme-duad geometry. 36,
• Synthetic geometry. 34,

T.

• Tangent line. 35,
• Tiling. 34, 34,
• Tiling, semi-regular. 34,
• Topology. 0,
• Transformation. 0,
• Trail. 29,
• Tree. 29,
• Triangle. 12,
• Trivial linear space. 8,
• Trivial subspace. 7,

U.

• Unital. 16, 16, 35,
• Unordered pair. 29,

V.

• Vertex. 29,
• Vertex class. 29,

W.

• Walk. 29,
• Walk, circular. 33,
• Walk, length of. 29,

X.

Y.

Z.