历史与综述
This is a letter to the editor concerning Semjon Adlaj's article "An eloquent formula for the perimeter of an ellipse", AMS Notices 59, 8 (2012), 1094-1099.
There are two standard ways of peeling an orange: either cut the skin along meridians, or cut it along a spiral. We consider here the second method, and study the shape of the spiral strip, when unfolded on a table. We derive a formula that…
This paper is devoted to Poincar\'e's work in probability. Though the subject does not represent a large part of the mathematician's achievements, it provides significant insight into the evolution of Poincar\'e's thought on several…
Short information about the conference in 1960 in Jerusalem is presented together with an interesting photo where we can find several famous mathematicians participated in this conference. To recognize the people on the photo and collect…
Hans Duistermaat was scheduled to lecture in the 2010 School on Poisson Geometry at IMPA, but passed away suddenly. This is a record of a talk I gave at the 2010 Conference on Poisson Geometry (the week after the School) to share some of my…
In this short note we give a glimpse of homotopy type theory, a new field of mathematics at the intersection of algebraic topology and mathematical logic, and we explain Vladimir Voevodsky's univalent interpretation of it. This…
The search for a geometric interpretation of the constrained brackets of Dirac led to the definition of the Courant bracket. The search for the right notion of a "double" for Lie bialgebroids led to the definition of Courant algebroids. We…
Some basic properties of the ring of integers $\mathbb{Z}$ are extended to entire rings. In particular, arithmetic in entire principal rings is very similar than arithmetic in the ring of integers $\mathbb{Z}$. These arithmetic properties…
The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.
Many of the theorems of real analysis, against the background of the ordered field axioms, are equivalent to Dedekind completeness, and hence can serve as completeness axioms for the reals. In the course of demonstrating this, the article…
Leopold Vietoris and Guido Hoheisel showed how the existence of $\lim_{x\to 0}\frac{\sin x}{x}$ can be derived from the trigonometric addition formulas. In this article two new proofs for this result are given. In addition it is discussed…
The game of Spot it(R) is based on an order 7 finite projective plane. This article presents a solitaire challenge: extract an order 7 affine plane and arrange those 49 cards into a square such that the symmetries of the affine and…
In this thesis we examined mathematical properties of Fibonacci numbers and applications of this numbers in the nature,geometry and economy.We obtained Golden section and proved some mathematical identities using Golden section. Infinity of…
We give a new and simple proof of the fact that a finite family of analytic functions has a zero Wronskian only if it is linearly dependent.
The treatise of Ab\=u Ja'far al-Kh\=azin (Xth century), entitled "Commentary on the introduction of the tenth book of the treatise of Euclid" ("tafs\={i}r sadr al-maq\={a}la al-'\={a}shira min kit\={a}b Uql\={i}dis") exists in eight…
We illustrate Archimedes' method using models produced with 3D printers. This approach allowed us to create physical proofs of results known to Archimedes and illustrate ideas of a mathematician who is known both for his for his mechanical…
This article deals with the construction of surfaces that are suitable for representing pentachords or 5-pitch segments that are in the same $T/I$ class. It is a generalization of the well known \"Ottingen-Riemann torus for triads of…
In this paper we analyze both the scientific activities of Cahit Arf, a Turkish mathematician, and the social context in which he worked. We also discuss his work and social environment leading to the discovery of Arf invariant, Arf rings,…
What is the first prime? It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers. To find the…
The basic theorems of vector calculus are illuminated when we replace the original 3 stooges of vector calculus: Grad, Div, and Curl, with combinatorial substitutes. In addition to providing simple proofs of Green's theorem and the…