Search results
Results from the WOW.Com Content Network
A generalization of the idea of geometric borders is the idea of fiat boundaries by which is meant any sort of boundary that does not track an underlying bona fide physical discontinuity (fiat, Latin for "let it be done", a decision). Fiat boundaries are typically the product of human demarcation, such as in demarcating electoral districts or ...
Euclidean geometry is a mathematical system ... to define the boundaries of the Euclidean system. ... of independent axioms from which the most important geometric ...
Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups can act non-trivially (that is, when the groups in question are realized as geometric symmetries or ...
Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land' and μέτρον (métron) 'a measure') [1] is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. [2]
It is a geometric space in which two real numbers are required to determine the position of each point. It is an affine space , which includes in particular the concept of parallel lines . It has also metrical properties induced by a distance , which allows to define circles , and angle measurement .
A form is an artist's way of using elements of art, principles of design, and media. Form, as an element of art, is three-dimensional and encloses space. Like a shape, a form has length and width, but it also has depth. Forms are either geometric or free-form, and can be symmetrical or asymmetrical.
In solid modeling and computer-aided design, boundary representation (often abbreviated B-rep or BREP) is a method for representing a 3D shape [1] by defining the limits of its volume. A solid is represented as a collection of connected surface elements, which define the boundary between interior and exterior points.
In modern geometry, a line is usually either taken as a primitive notion with properties given by axioms, [1]: 95 or else defined as a set of points obeying a linear relationship, for instance when real numbers are taken to be primitive and geometry is established analytically in terms of numerical coordinates.