While mandible proportions do not appear to constrain permanent molar initiation times, how adequate space is created in the corpus for these teeth in a timely way is not well understood. This question is important for explaining how primate tooth and jaw development and evolution are coordinated. Landmark and linear measurement data were used to characterize mandible shape, growth trajectory, ...

The goal of paper is to present the magnetic field calculations in high current bus ducts. Finiteelement method is used to do this. Bus ducts under study have figure such as circle area. Thecalculations will be using mathematical relations, meshed geometric shape and analyzing them.Geometric mean will help us to determine the value of magnetic field. COMSOL software is appliedfor simulation stu...

     Heat transfer mechanisms and the solidification process are simulated for a continuous casting machine and the geometric shape of the liquid pool is predicted considering different conditions. A heat transfer and solidification model is described for the continuous casting of steel slabs. The model has been established on the basis of the technical conditions of the slab caster in the con...

The connection between architecture and science and sound based on mathematical relations has continued to develop[ since the rise of the Western classical civilization that originated in Ancient Greece. The mysterious Pythagorean cosmology pursued as secret esoteric knowledge was related to the search of rhythm, proportionality and harmony. Even somewhat earlier, Greek mysteries were based on ...

Even if Computer-Aided Geometric Design modelers are now based on powerful mathematical models for curves and surfaces, there are important needs for tools to create, analyze and modify these objects. Designing product shapes with free-form curves and surfaces is still a tedious task and modifying the shape obtained is even more difficult and, most of the time, needs recreating a part up to the...

Abstract Analogy-making is at the core of human and artificial intelligence creativity with applications to such diverse tasks as proving mathematical theorems building theories, common sense reasoning, learning, language acquisition, story telling. This paper introduces from first principles an abstract algebraic framework analogical proportions form ‘ a b what c d ’ in general setting univers...

This paper considers the birth of algebraic proof by looking at the works of Cardano, Viète, Harriot and Pell. The transition from geometric to algebraic proof was mediated by appeals to the Eudoxan theory of proportions in book V of Euclid. The crucial notational innovation was the development of brackets. By the middle of the seventeenth century, geometric proof was unsustainable as the sole ...

This paper describes the application of geometric concepts for data retrieval and proposes a geometric model for accessing and manipulating multidimensional data in relational databases. A geometric query model is proposed for the queries based on locations of geometric objects. In the geometric query model, the data from the database are interpreted geometrically as multidimensional geometric ...

In a corpus study we found that authors vary both mathematical form and precision1 when expressing numerical quantities. Indeed, within the same document, a quantity is often described vaguely in some places and more accurately in others. Vague descriptions tend to occur early in a document and to be expressed in simpler mathematical forms (e.g., fractions or ratios), whereas more accurate desc...

A geometric modeller is a piece of software allowing to create, manipulate and modify geometric objects. Modern geometric modellers usually use a mathematical model to represent objects and are developed around a kernel that proposes basic operations to create and manipulate objects called by high level operations. Because of these proceedings, the context is a priori in favour of the use of fo...