• Corpus ID: 120866868

G8,2 Geometric Algebra, DCGA

@article{Easter2015G82GA,
  title={G8,2 Geometric Algebra, DCGA},
  author={Robert Benjamin Easter},
  journal={viXra},
  year={2015}
}

• R. B. Easter
• Published 1 August 2015
• Mathematics
• viXra

The metric we use for G8;2 is (1; 1; 1; 1; i1; 1; 1; 1; 1; i1). This metric makes it very simple to use the CGA subalgebras of the CGA1 and CGA2 subspaces in a way fully compatible with CGA. These two CGAs are used as mirror copies or doubles to create bivector-valued entities for points and surfaces. As such, the G8;2 geo- metric algebra of these new bivector-valued point and surface entities could be called Double-Conformal Geometric Algebra (DCGA), or even Bi-conformal Geometric Algebra (Bi-CGA or 2-CGA). The G8;2 DCGA surface entities include all of the types of surface entities avail- able in G4;1 CGA and in the G6;3 geometric algebra (10) known as G6;3 Quadric Geometric Algebra (QGA) (2)(6). DCGA also includes a new toroid (torus) surface entity. All DCGA entities (both GIPNS and their GOPNS duals) can be rotated, isometrically dilated, and translated by versor operations on the entities. The DCGA rotor, dilator, and translator are each a new form of bi-versor or double-versor of multivector-grade four. The DCGA entities will refer to all entities of the DCGA algebra, and the bi-CGA entities will refer specically to the CGA-subset of entities (points, lines, circles, planes, and spheres) as they exist in DCGA. The CGA1 and CGA2 entities also exist within their CGA subalgebras, oering theexibility to use them separately, or also to double them to form bi-CGA entities when it is desired to bring them into the larger DCGA space.