历史与综述
In the study of the real projective plane, harmonic conjugates have an essential role, with applications to projectivities, involutions, and polarity. The construction of a harmonic conjugate requires the selection of auxiliary elements; it…
We examine the preparation and context of the paper "The Crisis in Contemporary Mathematics" by Errett Bishop, published 1975 in Historia Mathematica. Bishop tried to moderate the differences between Hilbert and Brouwer with respect to the…
During the early 1830's Bernard Bolzano, working in Prague, wrote a manuscript giving a foundational account of numbers and their properties. In the final section of his work he described what he called `infinite number expressions' and…
A common objection to the definition of intuitionistic implication in the Proof Interpretation is that it is impredicative. I discuss the history of that objection, argue that in Brouwer's writings predicativity of implication is ensured…
There is little known about the methods used by the ancient Babylonians and Egyptians to arrive at their recorded estimates of the value of Pi. A surprisingly accurate estimate of Pi was recently revealed coded within a verse in the book of…
Kripke's Schema (better the Brouwer-Kripke Schema) and the Kreisel-Troelstra Theory of the Creating Subject were introduced around the same time for the same purpose, that of analysing Brouwer's 'Creating Subject arguments'; other…
In this article we discuss an important students' misconception about derivatives, that the expression of the derivative of the function contains the information as to whether the function is differentiable or not where the expression is…
This study aims to describe the communication of prospective teachers in learning mathematics. The research was conducted in SMAN 1 Madura. The subject of this research is PLP student from Mathematics Education Study Program of Madura…
A very old problem in campanology is the search for peals. The latter can be thought of as a heavily constrained sequence of all possible permutations of a given size, where the exact nature of the constraints depends on which method of…
We discuss the presence of symmetries in images engraved on ancient seals, in particular on stamp seals. Used to stamp decorations, to secure the containers from tampering and for owner's identification, we can find seals that can be dated…
Breaking a line segment L in two places at random, the three pieces can be configured as a triangle T with probability 1/4. We determine both the PDF and CDF for area(T) in terms of elliptic integrals. In particular, if L has length 1, then…
Defined by a single axiom, finite abstract simplicial complexes belong to the simplest constructs of mathematics. We look at a a few theorems.
If there is a "platonic world" M of mathematical facts, what does M contain precisely? I observe that if M is too large, it is uninteresting, because the value is in the selection, not in the totality; if it is smaller and interesting, it…
Morley's Theorem about angle trisectors can be viewed as the statement that a certain diagram `exists', meaning that triangles of prescribed shapes meet in a prescribed pattern. This diagram is the case n=3 of a class of diagrams we call…
These notes aim to give a gentle account to one approach to the theory of finite sets without making use of the natural numbers. They were written to be used as the basis for a student seminar. There are no real prerequisites except for a…
We present a motivating example for matrix multiplication based on factoring a data matrix. Traditionally, matrix multiplication is motivated by applications in physics: composing rigid transformations, scaling, sheering, etc. We present an…
We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.
This article shows how to find the solution of an arbitrary quintic equation by performing two simultaneous folds on a sheet of paper. The folds achieve specific incidences between a set of points and lines that are determined by the…
Exponential distributions appear in a wide range of applications including chemistry, nuclear physics, time series analyses, and stock market trends. There are conceivable circumstances in which one would be interested in the cumulative…
This article describes the authors' teaching experience in flipping the class of a basic undergraduate mathematics course Introductory Linear Algebra. We utilize a full-featured free electronic textbook, online lecture notes, an intranet…