[ 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
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
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
'time is a flat circle'? what are you talking about, all circles are flat
Equivalent latitude (Climatology 🌍)
In differential geometry, the equivalent latitude is a Lagrangian coordinate. It is often used in atmospheric science, particularly in the study of stratospheric dynamics. Each isoline in a map of equivalent latitude follows the flow velocity and encloses the same area as the latitude line of equivalent value, hence "equivalent latitude."...
https://en.wikipedia.org/wiki/Equivalent_latitude
#EquivalentLatitude #Climatology #DifferentialGeometry #Equivalence
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