Related papers: Early-Dynastic tables from Southern Mesopotamia, o…
Conceptual landscapes in Egypt show a remarkable continuity - for as long as 2000 years - in the use of symbols and in the interplay between natural and man-built features. Directionality, both in the sense of succession of elements and of…
One of the most powerful ideas in the study and classification of algebraic varieties is the notion of a model: that is, to single out an object, in the appropriate isomorphism class, with nice properties. This survey aims to define and…
A mean-field theory is developed for the scale-invariant length distributions observed during the coarsening of one-dimensional faceted surfaces. This theory closely follows the Lifshitz-Slyozov-Wagner theory of Ostwald ripening in…
A common numerical task is to represent functions which are highly spatially anisotropic, and to solve differential equations related to these functions. One way such anisotropy arises is that information transfer along one spatial…
Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
In this article we consider surfaces in the product space $\h^2\times \r$ of the hyperbolic plane $\h^2$ with the real line. The main results are: a description of some geometric properties of minimal graphs; new examples of complete…
We consider the number of configurations of a surface in two dimensions that has a prescribed length and encloses a prescribed perimeter with respect to a baseline. An approximate analytical treatment in a semi--continuum compares…
This article describes the accurateness of our application namely Self-Developed Aesthetics Measurement Application (SDA) in measuring the aesthetics aspect by comparing the results of our application and users' perceptions in measuring the…
Available algorithms for the initialization of volume fractions typically utilize exact functions to model fluid interfaces, or they rely on computationally costly intersections between volume meshes. Here, a new algorithm is proposed that…
In this paper we compute the distributions of various markings on smooth cubic surfaces defined over the finite field $\mathbb{F}_q$, for example the distribution of pairs of points, `tritangents' or `double sixes'. We also compute the…
Signed distance fields (SDFs) are a widely used implicit surface representation, with broad applications in computer graphics, computer vision, and applied mathematics. To reconstruct an explicit triangle mesh surface corresponding to an…
The developable surface is an important surface in computer aided design, geometric modeling and industrial manufactory. It is often given in the stan- dard parametric form, but it can also be in the implicit form which is commonly used in…
Square-tiled surfaces are a class of translation surfaces that are of particular interest in geometry and dynamics because, as covers of the square torus, they share some of its simplicity and structure. In this paper, we study counting…
In this paper I shall show that the formula 0:4,48 times circumference squared for the area of a circle, which occurs in a few Babylonian mathematical texts, can be traced back to at the latest the twenty-third century BCE.
In this article, we study the inscription on the reverse of Susa Mathematical Text No.\,2, a clay tablet held in the collection of the Louvre Museum and thought to date from between 1894--1595 BC. We focus on the formula given in this text…
We present a method for computing all the symmetries of a rational ruled surface defined by a rational parametrization which works directly in parametric rational form, i.e. without computing or making use of the implicit equation of the…
In an earlier work we identified the types and numbers of static equilibrium points of solids arising from fine, equidistant $n$-discretrizations of smooth, convex surfaces. We showed that such discretizations carry equilibrium points on…
Pebbles (calculos in Latin) are the "bits" used in the Ancients' four function calculator / computer. The Ancient Computer's normal mode is to work with numbers in what we would call exponential notation. Decimal numbers can have up to 10…
Thousands of first-millennium BCE ivory carvings have been excavated from Neo-Assyrian sites in Mesopotamia (primarily Nimrud, Khorsabad, and Arslan Tash) hundreds of miles from their Levantine production contexts. At present, their…