历史与综述
Hilbert's Foundations of Geometry was perhaps one of the most influential works of geometry in the 20th century and its axiomatics was the first systematic attempt to clear up the logical gaps of the Elements. But does it have gaps of its…
The Hebrew Calendar is based on very deep and complicated mathematics, involving diophantine approximation, but it is very surprising that the gaps between consecutive Christmas-in-Hanukkah years is always a member of the set {2,3,5,8}.…
This is an English translation of Felix Klein's classical paper "\"Uber die Aufl\"osung der allgemeinen Gleichungen f\"unften und sechsten Grades (Auszug aus einem Schreiben an Herrn K. Hensel)" from 1905 and is put in modern notation. The…
This paper deals with the algebraic structure of the sequence of harmonics when combined with equal temperaments. Fractals and the golden ratio appear surprisingly on the way. The sequence of physical harmonics is an increasingly enumerable…
If $P$ is a point inside $\triangle ABC$, then the cevians through $P$ divide $\triangle ABC$ into six small triangles. We give theorems about the relationships between the radii of the circumcircles of these triangles. We also state some…
Penrose tilings and Arabic Mathematical explorations. One single article published in the 2010 HOM-SIGMAA publication by the Mathematical Association of America.
We show any power of five may be expressed arithmetically with the digits of its decimal representation. We also show powers of five (in decimal) contain any amount of zeros in a row.
Mathematical concepts and results have often been given a long history, stretching far back in time. Yet recent work in the history of mathematics has tended to focus on local topics, over a short term-scale, and on the study of ephemeral…
This article describes what can happen when sustained effort and resources are devoted to creating a teacher professional support and development organization that puts teachers' needs first. Over the last ten years, Math for America Los…
We present a study of the implementation of the Electronic Preparatory Test for beginning undergraduates reading mathematics. The Test comprises two elements: diagnostic and self-learning. The diagnostic element identifies gaps in the…
We give an excellent approximation of the average number of spins of a simplified version of a two-player version of the game Dreidel. We also make a conjecture on the average number of spins of the full version of the game.
We correct a common (but mistaken) attribution of the evaluation of the probability integral, usually attributed to Poisson, Gauss, or Laplace.
It is well known that Heron's theorem provides an explicit formula for the area of a triangle, as a symmetric function of the lengths of its sides. It has been extended by Brahmagupta to quadrilaterals inscribed in a circle (cyclic…
An obituary for Alexander Gordon which will appear in the Journal of Spectral Theory
Sir Michael Atiyah was considered as one of the world's foremost mathematicians, He is best known for his work in algebraic topology and the co-development of a branch of mathematics called topological K-theory together with the…
Crochet models of a hyperbolic plane is a popular educational tool as they help to visualize complicated objets in hyperbolic geometry. We present another way how to make crochet models when we view them as a part of a triangulated…
"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…
In this paper we present geometry of some curves in Taxicab metric. All curves of second order and trifocal ellipse in this metric are presented. Area and perimeter of some curves are also defined.
In this paper we present a method for extraction of arcs of the algebraic curves of the higher order. Method is applied on conics, Cartesian ovals, trifocal curves and generalized Weber's curve.
In this paper we consider historical genesis of trifocal curve as an optimal curve for solving the Fermat's problem (minimizing the sum of distance of one point to three given points in the plane). Trifocal curves are basic plane geometric…