What is the Hyperbolic Plane really like? скачать в хорошем качестве

What is the Hyperbolic Plane really like?

#SoMEpi === Resources === Note: so... apparently YouTube doesn't let small channels put external links in the description... so for the moment, some of the promised links will be a "google and you shall find"... sorry about that... :/ -Steve Trettel's Foundations of Geometry (the main resource of this video)(available directly on the web) -Veritasium Non-Euclidean History Video:    • How One Line in the Oldest Math Text Hinte...   -For learning about curvature:    • The clever way curvature is described in math   -A good serie about topology and manifolds, for those who want to go deep and abstract:    • Manifolds   -"Noneuclid". A website that shows an interactive version of the map we did in this video. It also contains info about how to code it. -For the construction involving the tractoid and its map, search for the book "Visual Complex Analysis", by Tristan Needham. I don't know of a free resource that explains it... sorry... -For the Hyperboloid Model, search a paper called "Hyperbolic Geometry on a Hyperboloid" -For the crochet model, the book "Crocheting Adventures with Hyperbolic Planes" by Daina Taimina is basically straight from the original source, and goes very much detail. There's also a video explaining how to make it:    • Make Your Own Hyperbolic Surface!   -For the "forced tesselations", search for example "hyperbolic soccer ball" -Hyperbolica devlogs:    • Hyperbolica   -The page for the game HyperRoge. LOTS of hyperbolic geometry explanations there. The game is also free! -For those of you wanting to do vector-like stuff in hyperbolic geometry: search for gyrovector space. There isn't much info online about them though... main resources are the books and papers of Abraham A. Ungar (they are very formal, you've been warned) and a website resuming some of the formulas and extending them to the sphere (search "kappa stereographic model") === Chapters === 0:00 Intro 3:04 Chapter I: The Sphere 6:50 Chapter II: The Maps (and Intrinsic Geometry) 14:07 Chapter III: Uncovering the Hyperbolic Plane 19:11 Chapter IV: The Hyperbolic Plane 21:32 Extra: Alternative constructions of the Hyperbolic Plane 24:48 Ending === Corrections === (none yet) === Credits === Script, Animations and Editing: Alejandro García Voice: Jonathan García Music: Carlos Mauricio Reyes