Related papers: Huygens and $\pi$
We discuss Luigi Cremona's contribution to the early development of the theory of cubic surfaces.
We give explicit bounds on the intersection number between any curve on a tight multigeodesic and the two ending curves. We use this to construct all tight multigeodesics and so conclude that distances in the curve graph are computable. The…
Let $P\in \mathbb Z[X]\setminus\{0\}$ be of degree $\delta\ge 1$ and usual height $H\ge 1$, and let $\alpha\in \overline{\mathbb Q}^*$ be of degree $d\ge 2$. Mahler proved in 1931 the following transcendence measure for $e^\alpha$: for any…
In 1989, D. Happel pointed out for a possible connection between the global dimension of a finite-dimensional algebra and its Hochschild cohomology: is it true that the vanishing of Hochschild cohomology higher groups is sufficient to…
In 1640's, Blaise Pascal discovered a remarkable property of a hexagon inscribed in a conic - Pascal Theorem, which gave birth of the projective geometry. In this paper, a new geometric invariant of algebraic curves is discovered by a…
Schroedinger's famous quadruple of factorizations of the hypergeometric equation is archived here
"The mathematization of time has limits," writes Derrida in Ousia and Gramme. Taking this quote in all possible senses, this paper considers Derrida's definition of limit as gramme, trace, and aporia, and develops the mathematization of all…
The $\pi$-series is attributed to Madhava, Gregory and Leibniz based on the chronology of its discovery. While this acknowledges the fact that Madhava of Sangamagrama an Indian mathematician who lived in Kerala in the 14th century along the…
The notion of the magnitude of a metric space was introduced by Leinster in [8] and developed in [10], [9], [11] and [16], but the magnitudes of familiar sets in Euclidean space are only understood in relatively few cases. In this paper we…
Homogeneous spaces are de Branges' Hilbert spaces of entire functions with the property that certain weighted rescaling transforms induce isometries of the space into itself. A classical example of a homogeneous space is the Paley-Wiener…
The goal of this paper is to experiment new math concepts and theories, especially if they run counter to the classical ones. To prove that contradiction is not a catastrophe, and to learn to handle it in an (un)usual way. To transform the…
In a fascinating recent American Mathematical Monthly article, Norman Wildberger and Dean Rubine introduced a new kind of combinatorial numbers, that they aptly named the ``Geode numbers''. While their definition is simple, these numbers…
One unsolved mathematical problem remains the perfect cuboid problem. A perfect cuboid is a rectangular parallelepiped whose edges, face diagonals and space diagonal are all expressed as integers. No such cuboid has yet been discovered and…
A famous pre-Newtonian formula for $\pi$ is obtained directly from the variational approach to the spectrum of the hydrogen atom in spaces of arbitrary dimensions greater than one, including the physical three dimensions.
Transcript of G.J. Chaitin's 2 March 2000 Carnegie Mellon University School of Computer Science Distinguished Lecture. The notion of randomness is taken from physics and applied to pure mathematics in order to shed light on the…
Even though it has been almost a century since quantum mechanics planted roots, the field has its share of unresolved problems. It could be the result of a wrong mathematical structure providing inadequate understanding of the quantum…
Ancient astronomers faced the problem of dealing with arcs and angles in their observations and predictions without the help of modern trigonometry. The usual method to deal with such problems was the Menelaus Theorem, explicitly discussed…
In this note we investigate the asymptotic behavior of the number of maximum modulus points, of an entire function, sitting in a disc of radius $r$. In 1964, Erd\Humlaut{o}s asked whether there exists a non-monomial function so that this…
In 1981 W.L. Edge discovered and studied a pencil $\mathcal{C}$ of highly symmetric genus $6$ projective curves with remarkable properties. Edge's work was based on an 1895 paper of A. Wiman. Both papers were written in the satisfying style…
Varieties without deformations are defined over a number field. Several old and new examples of this phenomenon are discussed such as Bely\u \i\ curves and Shimura varieties. Rigidity is related to maximal Higgs fields which come from…