Physics notes

Applying Hilbert curves to geocodes johndcook.com/blog/2022/06/0…

Every C^1 differential structure on a manifold can be uniquely smoothed to a C^∞ differential structure. -- Whitney, 1936

If a triangle has sides a, b, c and area Δ, then a² + b² + c² ≥ 4 √3 Δ. -- Weitzenböck's inequality

Conway's proof of the classification of surfaces new.math.uiuc.edu/zipproof/zippr… [pdf]

Riemann-Roch theorem en.wikipedia.org/wiki/Riemann%E…

Notes on introductory point-set topology pi.math.cornell.edu/~hatcher/Top/T…

Trig in hyperbolic geometry johndcook.com/blog/2022/09/0…

Topology and geometry software geometrygames.org

The maximum number of mutually touching spheres in R^n is n+2.

Proto-Penrose tilings cp4space.wordpress.com/2015/02/19/pro…

Open problems in topology openproblemgarden.org/topology

The topological part of my brain Finds Möbius strips quite a strain. But I make you this pledge: I’ll glue one at its edge And build a real projective plane. By Richard Elwes

The 3-sphere is a non-abelian Lie group whose multiplication is not even commutative up to homotopy.

The long line en.wikipedia.org/wiki/Long_line…

How medieval astronomers made trig tables johndcook.com/blog/2014/11/2…

Gauss-Bonnet theorem

Hadwiger's conjecture in combinatorial geometry en.wikipedia.org/wiki/Hadwiger_…

List of fractals by Hausdorff dimension en.wikipedia.org/wiki/List_of_f…

Exotic spheres: There are 28 smooth structures on the 7-sphere. (Milnor and Kervaire)