历史与综述
This is an expository article that results from a talk given to second year students at Oldenburg university. The aim of the talk was to show what beautiful and unexpected results may be obtained if one plays with daring analogies in a way…
This paper describes the work of Jesse Douglas on the Plateau problem, work for which he was awarded a Fields Medal in 1936, and considers the contributions Tibor Rado made in the 1930s.
E731 in the Enestrom index. Originally published as "Solutio problematis ob singularia calculi artificia memorabilis", Memoires de l'academie des sciences de St-Petersbourg 2 (1810), 3-9. For $z$ the distance from the origin, and $v$ a…
It is a survey of the results obtained by K. Glazek's and his co-workers. We restrict our attention to the problems of axiomatizations of n-ary groups, classes of n-ary groups, properties of skew elements and homomorphisms induced by skew…
In this paper we study the Three Hat Problem which appeared in Puzzle Corner of the Technology Review magazine. This puzzle gives a scenario in which three players wearing hats are sitting together and each hat can be seen by everyone…
How far off the edge of the table can we reach by stacking $n$ identical, homogeneous, frictionless blocks of length 1? A classical solution achieves an overhang of $1/2 H_n$, where $H_n ~ \ln n$ is the $n$th harmonic number. This solution…
In the Byzantine Empire of 11-15 CE chess was played on the circular board. Two versions were known - REGULAR and SYMMETRIC. The difference between them is easy: the white queen is placed either on light (regular) or on dark square…
Laplace's views on randomness and determinism. The paper was written for "Cahiers rationalistes" and addresses a rather wide audience. It contains large quotations of Laplace, most of them coming from his introduction to the book…
A characterization of real numbers constructible by paper folding.
Translated from the Latin original, "Observationes generales circa series, quarum termini secundum sinus vel cosinus angulorum multiplorum progrediuntur" (1777). E655 in the Enestrom index. Euler looks at the binomial expansion $(1+x)^n$…
We investigate the mathematics behind 1500 year old root extraction methods presented by Aryabhata in his famous mathematical treatise "Aryabhatiya". Also, we look at their computational complexity.
M. E. Cesaro (1885) gave a quite remarkable expression for the Bell number --the number of partitions of an n-element set -- as a definite integral. This note is an exposition, correcting a typographical error in the original.
This is an English translation of Euler's ``Theoremata circa residua ex divisione potestatum relicta'', Novi Commentarii academiae scientiarum Petropolitanae 7 (1761), 49-82. E262 in the Enestrom index. Euler gives many elementary results…
I propose a notion of theory motivated by Category theory.
The partisans of the hypothesis of the Indian origin of the numerals create confusion between the history of the Indian mathematics and the history of our modern numerals. To argue the thesis of the Indian origin of the numbers they…
The origin of the numerals that we inherited from the arabo-Islamic civilization remained one enigma. The hypothesis of the Indian origin remained, with controversies, without serious rival. It was the dominant hypothesis since more of one…
This is a historical survey, beginning where Atiyah and Sullivan leave off...
Translation from the Latin original, "Demonstratio gemina theorematis Neutoniani, quo traditur relatio inter coefficientes cuiusvis aequationis algebraicae et summas potestatum radicum eiusdem" (1747). E153 in the Enestrom index. In this…
This paper presents a simple geometrical fact which could relate to the history of mathematics and astronomy. This fact shows a natural link between the circle and the multiples of 6 and it makes it possible to obtain a simple…
I want to write about what I know and remember about the activities of Leonid Vital'evich Kantorovich, an outstanding scientist of the 20th century; about his dramatic struggle for recognition of his mathematical economic theories; about…