All Questions
Tagged with incidence-geometry mg.metric-geometry
7 questions
10
votes
1
answer
356
views
Is the group of translations of an affine plane always commutative?
$\DeclareMathOperator\Dil{Dil}\DeclareMathOperator\Trans{Trans}\DeclareMathOperator\Col{Col}$An affine plane is a set of points $X$ endowed with a family $\mathcal L$ of subsets of $X$, called lines, ...
- 42k
7
votes
1
answer
347
views
A corollary of the affine Desargues axiom
Definition 1. An affine plane is a pair $(X,\mathcal L)$ consisting of a set $X$ and a family $\mathcal L$ of subsets of $X$ called lines which satisfy the following axioms:
Any distinct points $x,y\...
- 42k
8
votes
1
answer
246
views
A vertical line with many intersections with $n$ non-parallel lines
Pick $n\ge 3$ non-vertical lines $\mathscr{L}:=\{\ell_1,\ldots,\ell_n\}$ in the plane which are pairwise non-parallel, and they are not all concurrent in a single point.
Question. Does there exist a ...
- 1,511
2
votes
0
answers
56
views
Classification of Moufang planes of real dimension 16
Incidence geometry is not really area of expertise so I'm asking here: are all Moufang planes of 16 dimension already classified?
I'm not just interested in the compact ones. Is there already a ...
- 295
5
votes
2
answers
1k
views
Geometric interpretation of $BN$-pairs
My question is relative to a geometric interpretation of the $BN$-pairs that arise in Tits' theory of buildings. Here is a definition that comes from an article by G. Stroth (Nonspherical spheres).
$[...
- 499
14
votes
0
answers
552
views
Who conjectured that a transitive projective plane is Desarguesian?
The only known finite projective plane with a transitive automorphism group is the Desarguesian plane $PG(2,q)$ and it seems likely that there are no others, although this is not (quite) proved.
...
- 12.7k
4
votes
0
answers
443
views
Intersection of pencils in $\mathcal{R}^2$
Consider $9n$ pencils through non-collinear points $p_1, \ldots , p_{9n}$ in $R^2$ each consisting of at most $n$ concurrent lines. Define the intersection $S$ of these pencils to be the set of points ...
