历史与综述
We show the results on the history of the invention of the conjugacy $h(x)=\frac{2}{\pi}\arcsin\sqrt{x}$ of one-dimensional $[0,\, 1]\rightarrow [0,\, 1]$ maps $f(x)=4x(1-x)$ and $g(x)=1-|1-2x|$.
About 160 years ago, the Italian mathematician Fa\`a di Bruno published two notes dealing about the now eponymous formula giving the derivative of any order of a composition of two functions. We reproduce here the two original notes, Fa\`a…
This is a tract on the art and practice of mathematical writing. Not only does the book cover basic principles of grammar, syntax, and usage, but it takes into account developments of the last twenty years that have been inspired by the…
It is pointed out that the language of quotient groups and wrapped distributions allows an elementary discussion of Benford's Law, and adds arguments supporting wide-spread observability of this statistics.
This is the editor's preface to the special issue of Journal of Spectral Theory, in memory of Yuri Safarov.
In this short paper, I introduce an elementary method for exactly evaluating the definite integrals $\, \int_0^{\pi}{\ln{(\sin{\theta})}\,d\theta}$, $\int_0^{\pi/2}{\ln{(\sin{\theta})}\,d\theta}$,…
Frederick William Gehring was a hugely influential mathematician who spent most of his career at the University of Michigan. Gehring's major research contributions were to Geometric Function Theory, particularly in higher dimensions…
Despite the increasing number of women graduating in mathematics, a systemic gender imbalance persists and is signified by a pronounced gender gap in the distribution of active researchers and professors. Especially at the level of…
Why are white and black piano keys in an octave arranged as they are today? This article examines the relations between abstract algebra and key signature, scales, degrees, and keyboard configurations in general equal-temperament systems.…
Nicolas-Auguste Tissot (1824--1897) published a series of papers on cartography in which he introduced a tool which became known later on, among geographers, under the name of the "Tissot indicatrix." This tool was broadly used during the…
This is an edition of the famous letter by Richard Dedekind to H. Keferstein dated 27 February 1890
The invention of non-Euclidean geometries is often seen through the optics of Hilbertian formal axiomatic method developed later in the 19th century. However such an anachronistic approach fails to provide a sound reading of Lobachevsky's…
In this expository paper written to commemorate Fibonacci Day 2016, we discuss famous relations involving the Fibonacci sequence, the golden ratio, continued fractions and nested radicals, and show how these fit into a more general…
In this paper, we introduce fiboquadratic sequences as an extension to infinity of the board of Rithmomachia and we prove that this extension gives raise to fiboquadratic sequences which we define here. Also, fiboquadratic sequences provide…
The content of this paper is the noted transcription of the 83 letters written by Enrico Betti between 1860 and 1886 stored at the Istituto Mazziniano, Museo del Risorgimento in Genova and now available at www.luigi-cremona.it The letters…
Two perpendicular segments which divide a given triangle into 4 regions of equal area is called a quadrisection of the triangle. Leonhard Euler proved in 1779 that every scalene triangle has a quadrisection with its triangular part on the…
We provide a mathematic model for the Traditional Yin-and-Yang Double Fish Diagram which from Chinese Traditional Philosophy.
We explore visual representations of tilings corresponding to Schl\"afli symbols. In three dimensions, we call these tilings "honeycombs". Schl\"afli symbols encode, in a very efficient way, regular tilings of spherical, euclidean and…
This is an English translation of the obituary notice by Beno Eckmann, appearing in Elemente der Mathematik 47.3 (1992) 118--122 (in German).
What initial trajectory angle maximizes the arc length of an ideal projectile? We show the optimal angle, which depends neither on the initial speed nor on the acceleration of gravity, is the solution x to a surprising transcendental…