Projective Geometry
Read this topicExplanations 2
- What does it mean for two lines to be parallel? We already know that with two parallel lines, one can be translated to the other. That means that as we go along one line, the ot…
By Vinjai Vale
- In Euclidean geometry, almost all lines intersect. That's right. But, wouldn't it be nice if parallel lines intersected? That's why we have a new type of geometry called project…
By Freya Edholm, Victor Wang
Problems 4
- Where do parallel lines intersect (in the projective plane)?
- Which Möbius transformation sends distinct points a,b,ca,b,ca,b,c in P1\mathbb{P}^1P1 to 0,1,∞0,1,\infty0,1,∞?
- Describe the stabilizer of i∈Hi\in \mathbb{H}i∈H within Aut(H)=PSL2(R)\operatorname{Aut}(\mathbb{H}) = \operatorname{PSL}_2(\mathbb{R})Aut(H)=PSL2(R). Denote an element of PS…
- Which conformal mapping identifies the upper half plane H\mathbb{H}H with the unit disk D\mathbb{D}D?