相关论文: Geometric and algebraic interpretation of primitiv…

A mathematically and culturally natural modification of Evart Bruins' explanation of the genesis of the numbers on the Old Babylonian tablet Plimpton 322 gives an economical accounting for the "missing pairs" in his reconstruction. When the…

We extend the notion of triangle to "imaginary triangles" with complex valued sides and angles, and parametrize families of such triangles by plane algebraic curves. We study in detail families of triangles with two commensurable angles,…

This article proves a Pythagoras-type formula for the sides and diagonals of a polygon inscribed in a semicircle having one of the sides of the polygon as diameter.

We investigate the ``generalized Heron polynomial'' that relates the squared area of an n-gon inscribed in a circle to the squares of its side lengths. For a (2m+1)-gon or (2m+2)-gon, we express it as the defining polynomial of a certain…

While geometry with transcendental curves, like the Quadratrix of Hippias and the Spiral of Archimedes, played a significant role in our modern developments of geometry and algebra. The investigation has fallen off in the modern era despite…

We give a few simple methods to geometically describe some polygon and chain-spaces in R^d. They are strong enough to give tables of m-gons and m-chains when m <= 6.

The right triangles represented in the Plimpton 322 data have integer sides $(a, b, d)$ with $a < b < d$, by inspecting the data we propose $b=M\,Q_{M}$ with $M,Q_{M}$ positive integers. In this way we present a new data-driven family of…

Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…

We observe structure in the sequences of quotients and remainders of the Euclidean algorithm with two families of inputs. Analyzing the remainders, we obtain new algorithms for computing modular inverses and representating prime numbers by…

We geometrically prove that in a d-dimensional cube with edges of length n, the number of particular d-dimensional tetrahedrons are given by Eulerian numbers. These tetrahedrons tassellate the cube, In this way the sum of the cubes are the…

The article presents a new approach to euclidean plane geometry based on projective geometric algebra (PGA). It is designed for anyone with an interest in plane geometry, or who wishes to familiarize themselves with PGA. After a brief…

Grassmann angles improve upon similar concepts of angle between subspaces that measure volume contraction in orthogonal projections, working for real or complex subspaces, and being more efficient when dimensions are different. Their…

In this paper geometry is studied with a novel approach. Every geometrical object is defined as a symbol which satisfies some properties. These symbols are then coded into a class of numbers which are named here as many dots numbers (MDN).…

Attention is focused on antisymmetrized versions of quantum spaces that are of particular importance in physics, i.e. two-dimensional quantum plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski…

We introduce the set of framed convex polyhedra with N faces as the symplectic quotient C^2N//SU(2). A framed polyhedron is then parametrized by N spinors living in C^2 satisfying suitable closure constraints and defines a usual convex…

An idea to present a classical Lie group of positive dimension by generators and relations sounds dubious, but happens to be fruitful. The isometry groups of classical geometries admit elegant and useful presentations by generators and…

Computation of Gauss's arithmetic-geometric mean involves iteration of a simple step, whose algebro-geometric interpretation is the construction of an elliptic curve isogenous to a given one, specifically one whose period is double the…

Let $\mathfrak g$ be an infinite-dimensional Lie algebra and $G$ be the algebraic completion of its module. Using a geometric interpretation in terms of sewing two Riemann spheres with a number of marked points, we introduce a…

In this article, we study the geometry of plane curves obtained by three sections and another section given as their sum on certain rational elliptic surfaces. We make use of Mumford representations of semi-reduced divisors in order to…

Generalised Pythagorean triples are integer tuples $(x,y,z)$ satisfying the equation $E_{a,b,c}: ax^2+by^2+cz^2=0$. A significant amount of research has been devoted towards understanding generalised Pythagorean triples and, in particular,…