历史与综述
An interesting conic section problem involving the maximum generalized golden right triangle $T_2$ is solved, and two simple constructions of $T_2$ are shown.
Beyond the difficulty to give true practical motives to introduce a theorem, the didactic transposition of scholarly knowledge in a school setting often leads to freezing a technical tool into a theorem given under minimal assumptions.…
An interesting problem that determine a triangle of smallest area which circumscribes a semicircle is solved. Then a generalized golden right triangles sequence $T_n$ is obtained, and an interesting construction of the maximum generalized…
Egbert Brieskorn died on July 11, 2013, a few days after his 77th birthday. He was an impressive personality who has left a lasting impression on all who knew him, whether inside or outside of mathematics. Brieskorn was a great…
In this Note, we start off with the primary representation of e and from there present an elementary short proof for the Wallis formula for $\pi$.
A special theorem related to the Fagnano's problem is proved and an example of the theorem is shown in a golden rectangle.
This article provides a brief introductory account of the theory of aperiodic order.
A survey of tessellations, which appeared in Italian in La Matematica vol 3 in 2010. The Tiling Lemma appears for the first time.
The content of this paper is the noted transcription of the 48 letters that Celeste Clericetti wrote to Luigi Cremona and the 10 letters that Cremona wrote to Clericetti between 1871 and 1887. The correspondence is stored at the Istituto…
In 2007, a new variety of the well-known problem of identifying a counterfeit coin using a balance scale was introduced in the sixth International Kolmogorov Math Tournament. This paper offers a comprehensive overview of this new problem by…
Integration by parts (IBP) has acquired a bad reputation. While it allows us to compute a wide variety of integrals when other methods fall short, its implementation is often seen as plodding and confusing. Readers familiar with tabular IBP…
Inspired by the relation between the algebra of complex numbers and plane geometry, William Rowan Hamilton sought an algebra of triples for application to three dimensional geometry. Unable to multiply and divide triples, he invented a…
A brief historical introduction for the enigmatic number Zero is given. The discussions are for popular consumption.
The Heesch problem 'grades' polygons that fail to tile the plane in terms of the number of layers (or corollas) of copies of it that can be formed around a central unit. We study the different topology of ' walls', which we define to be…
The dominant part in the mental calculation of the day of the week for any given date is to determine the year share, that is, the contribution of the two-digit year part of the date. This paper describes a number of year share computation…
We have found some patterns in some triangles.
In November 2014 Alexander Grothendieck passed away at the age of 86. There is no doubt that he was one of the greatest and most innovative mathematicians of the 20th century. After a bitter childhood, his meteoric ascent started in the…
These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is…
For the past five years advanced students have developed projects for our redesigned Calculus II classes to use. Our student project designers are often mathematically early in their careers, and so this provides them with an opportunity to…
The study of existence and uniqueness of solutions became important due to the lack of general formula for solving nonlinear ordinary differential equations (ODEs). Compact form of existence and uniqueness theory appeared nearly 200 years…