[ Lumo Kaŭstikaĵo ]
Matematika diferenciala geometrio priskribanta la ebenan koverton de kurboj spuritaj de radioj disvastiĝantaj tra manifoldo. 🤓 #nerd
~briletanta~
\eZ
#miksang #dailypic #aphotoaday
#Esperanto #photography #photo
#physics #optics #mathematics #maths
#caustics #differentialgeometry
#manifold #manifolds
#shimmering
RE: https://mathstodon.xyz/@oantolin/115956880232782872
this is the reason why i re-wrote the #differentialgeometry book of a course and gave it freely to anybody, the unavailability of exercises' solutions is really the worst thing a #textbook can show
A ball is 3D. A sphere is the surface of a ball and is only 2D. It has just 2 coördinates for every point, latitude and longitude (i.e. θ and φ without r).
I know that @standupmaths has definitely covered this particular one. I've seen Matt do it. This is Key Stage 3 National Curriculum #maths as taught in secondary school.
As I said, you've got a loudness of teeth grinding metric for how many mathematicians are in your readership who can further take that beyond KS3 to the 2 centuries of maths built from Karl Freidrich #Gauss and others that are some of the underpinnings of 20th century relativistic #physics.
I don't know whether you have a metric for the number of physicists in your readership. Physicists's teeth tend to start out frictionless, perfectly cuboid, inertial, and in vacuo. (-:
@oantolin @mapasmilhaud
#DifferentialGeometry #topology #curvature #cartography
https://www.shokabo.co.jp/mybooks/ISBN978-4-7853-1571-9.htm
Manifolds from Concrete Examples
by Atsushi Fujioka
Everyone says \(S^2\) “needs” \(\mathbb{R}^3\) for embedding.
But if the metric, not the coordinate count, carries curvature — what are we *actually* embedding?
A small note on why \(S^2 \subset \mathbb{R}^2\) may be more precise than it sounds.
⚙️🌀
#Geometry #Topology #DifferentialGeometry #Mathematics #PhilosophyOfMath #MathThought #Foundations #ModelingMindset
I'm finishing a book on geometrical tensor calculus, and in the last chapter there're sophisticated stuff like the exterior covariant derivative and similar. Some laws of physics that are typically taught without this formalism are shown in this formalism, but there's much material in few pages (you know, it's the last chapter).
Do you know of a book that presents classical physics in this language? I know that Thorne & Blandford's "Modern Classical Physics" uses tensors, but I'm not sure if it uses sophisticated stuff like an exterior covariant derivative (I don't have a copy). #physics #differentialgeometry #tensors
Change my mind: pseudogroups are the "wrong way" to formalize differential geometry.
What's wrong with formalizing charts and atlases, then a manifold is a set equipped with a maximal atlas?
We could formalize, e.g., complex manifolds using G-structures.
What is wrong with this approach?
Differential Geometry: A First Course in Curves and Surfaces [pdf]
https://math.franklin.uga.edu/sites/default/files/users/user317/ShifrinDiffGeo.pdf
#HackerNews #DifferentialGeometry #Curves #Surfaces #MathEducation #PDF #Resources
Got a reprint of this classic earlier this month. Good memories of learning exterior products for the first time from this. I wish/hope someone writes a biography of Spivak, always fascinates and inspires to know about people who dedicated their life to see the universe through the keyhole of a specific area. Spivak did that for all things related to geometry. A rare persona, and much rarer today.
Real-life application of the Theorema Egregium https://en.wikipedia.org/wiki/Theorema_Egregium
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