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Plane-based geometric algebra is an application of Clifford algebra to modelling planes, lines, points, and rigid transformations. Generally this is with the goal of solving applied problems involving these elements and their intersections , projections , and their angle from one another in 3D space. [ 1 ]
In this article, certain applications of the dual quaternion algebra to 2D geometry are discussed. At this present time, the article is focused on a 4-dimensional subalgebra of the dual quaternions which will later be called the planar quaternions. The planar quaternions make up a four-dimensional algebra over the real numbers.
Pages in category "Geometric algebra" The following 22 pages are in this category, out of 22 total. ... Plane-based geometric algebra; Plücker coordinates;
The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1 and is therefore a constructible number. In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length | | can be constructed with compass and straightedge in a finite number of steps.
In mathematics, a geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is built out of two fundamental operations, addition and the geometric product. Multiplication of vectors results in higher-dimensional objects called multivectors ...
In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is used, so the Euclidean plane refers to the ...
The algebra is not a field since the null elements are not invertible. All of the nonzero null elements are zero divisors. Since addition and multiplication are continuous operations with respect to the usual topology of the plane, the split-complex numbers form a topological ring. The algebra of split-complex numbers forms a composition ...
Quadric (algebraic geometry) Dimension of an algebraic variety; Hilbert's Nullstellensatz; Complete variety; Elimination theory; Gröbner basis; Projective variety; Quasiprojective variety; Canonical bundle; Complete intersection; Serre duality; Spaltenstein variety; Arithmetic genus, geometric genus, irregularity; Tangent space, Zariski ...