Geometry General

>>8935261
So I want to show that the set of directed line segments forms a vector space, but I'm not sure how to show that the scaling transform(is that the right word?) forms a field.

Anybody seen Vaughan Pratt's algebraicization of Euclid's axioms? It's a big conceptual advance IMO. Did he publish a real paper on it yet?

>>8936371
how does your addition work ?

>>8936567
How does that improve over Tarski's axiomatization using first-order logic?

(Tarski's axioms are in Section 2 of https://arxiv.org/pdf/1306.0066.pdf)

>>8936593
They're basically the traditional vectors from baby's first mechanics.

apply an affine transformation to the second segment so that it's beginning is coincident with end of the first segment.
The summation of the two segments is the directed segment from the beginning first segment to the end of the second segment (under the previous transformation).

>>8936609
this is not commutative, the neutral element works only on one side etc.

Is anyone by chance well versed in the theory of probability measures on Riemannian manifolds and related constructions like https://en.wikipedia.org/wiki/Wasserstein_metric? It's kind of a hot topic at the moment, so any nice introductory papers/books recs would be very nice.

how does one /gitgud/ at geometry?
what books? Interested in all geometries btw (euclidean, projective, hyp, diff, algebraic, topology maybe)

>>8936603
Because it's algebraic, genius. None of those shitty quantifiers.

Plus it turns the parallel postulate into an interchange law which is cool.

>>8936721
>topology maybe

Topology is a necessary prereq to any serious geometry. Considering a geometric space (manifold, variety, scheme) is a topological space with some additional structure.

>>8937556
I have taken topology in the past, I meant like, maybe a req on something in particular

>>8935261
I have the intention to study differential geometry this summer, anybody as good texts, online classes, or their old syllabuses?

File: order 3 projective plane.gif (22KB, 500x436px) Image search: [Google]

22KB, 500x436px

Where my finite geometry peeps at?

>>8936918
>Plus it turns the parallel postulate into an interchange law which is cool.

That does indeed sound cool. While I don't typically give a fuck about algebra I am down with purely categorical approaches to shit. Would appreciate a reference if you've got one.

>>8937669
"Differential Geometry: Curves,Surfaces,Manifolds" by Kühnel for classical diff. geom. and an introduction to Riemannian geometry.


"Introduction to Smooth Manifolds" by Lee, although that is more analysis and topology then it is geometry.

"Riemmanian Geometry and Geometric Analysis" by Jost for exactly what the title says. Should know fundamentals of manifolds and some PDE stuff first though.

>>8936721
>>8937669
Topology and Geometry - Breddon

>>8938316
does this guy have any other photos at all

>>8939314
probably not

File: shinu2.jpg (7KB, 196x257px) Image search: [Google]

7KB, 196x257px

>>8939596
>>8939314
rare shinu