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Fillmore showed that there are sets of constant width in $\mathbb R^d$ with analytic boundaries which have a trivial symmetry group (so these are very different from spheres; see "Symmetries of surfac …

A proof of the enumeration theorem for the Archimedean solids (which basically dates back to Kepler) can be found in the beautiful book "Polyhedra" by P.R. Cromwell (Cambridge University Press 1997, p …

A model equation for an inextensible, flexible, heavy surface in a gravitational field was deduced by Poisson Lagrange and later the problem was also studied by Poisson (see the references in the link …

Such a definition (but not the definition, I suppose) can be found in Clifford Algebras and the Classical Groups by Ian Porteous (see Chapt. 13). It is based on the classification of real algebra an …

Let $E$ and $E'$ be Banach spaces. Mappings $f:E\to E'$, which satisfy the inequality $$\|f(x + y) − f(x) − f(y)\| \leq\epsilon$$ for all $x, y \in E$, are called $\epsilon$-additive (or approximate …

Grünbaum and Shephard suggest that the winding numbers (for closed polygons) have been discussed in the literature at least since 1769. See A.L.F. Meister, Generalia de genesi figurarum planarum …

From the introduction to History of the Central Limit Theorem: From Laplace to Donsker by Hans Fischer: The term “central limit theorem” most likely traces back to Georg Pólya. As he recapitulat …

"Topological Vector Spaces" by Helmut Schaefer contains a thorough treatment of the classical Krein-Rutman theorem for compact positive operators in an ordered Banach space along with several general …

There is a bunch of such statements which can be obtained by Stein's method. You might be interested in the paper "On the Rate of Convergence in the Multivariate CLT" by Gotze, which is specifically …

"The determination of Gauss sums" by Berndt and Evans (Bull. Amer. Math. Soc., Vol. 5, Number 2 (1981), 107-129.) contains an exposition of the original proof due to Gauss. It also includes a short hi …

There exist several known global implicit function theorems. Those results tend to be tailored for specific applications. It seems to be rather difficult to state a universally useful one-size-fits-al …

A.F. Leont'ev continued to work on general Dirichlet series well into 1980s (until his death in 1987). Actually, he published three monographs on the subject from 1976 to 1983! He made a short summary …

This is a very old problem and there is a classical analytic approach to it. You can express the volume of sections of a convex body in terms of the Fourier transform of powers of the Minkowski functi …

This follows from the fact that the set of $n\times n$ matrices with simple spectrum is dense in the space of all $n\times n$ matrices ${\bf M}_n(\mathbb C)$ (or that the set of polynomials of degree …

How about Basic Geometry and Basic Geometry - Manual for Teachers by George D. Birkhoff and Ralph Beatley? In the spring of 1923, Professor Birkhoff was invited to deliver in Boston a series o …