Geometry

Evrende Dik Açı Kavramı Üzerine (On the Concept of Right Angles in the Universe)

Authors: Mesut Kavak
Comments: 8 Pages.

Alan, herhangi bir boyutta ve yönde hareketin oluşması için zorunlu ön koşullardan biridir. Hareketin hızı ve bunun bir süre içerisinde yapıldığı zamana bağlıdır. Herhangi bir boyutta hareket kabiliyeti, yalnızca buna müsade eden bir fiziksel ortam olduğu sürece olanaklı olur. Aksi halde diğer hareket unsurları da oluşmayacaktır. Peki alanı hangi kurallar yönetir?

Field is one of the necessary prerequisites for movement of any size and direction to occur. It depends on the speed of the movement and the time it is done within a period of time. Mobility in any dimension is possible only as long as there is a permissive physical environment. Otherwise, other movement elements will not occur. So what rules govern the space?
Category: Geometry

Deriving the Spherical Pythagorean Theorem Using Infinitesimal Area

Authors: Russell P. Patera
Comments: 3 Pages.

The Spherical Pythagorean Theorem is derived by performing an infinitesimal rotation of a spherical right triangle about a vertex not containing the right angle. The infinitesimal areas swept out by the sides of the spherical triangle are easily computed and used to derive the Spherical Pythagorean Theorem.
Category: Geometry

Location and Radius of a Triangle's Incircle Via Geometric Algebra

Authors: James A. Smith
Comments: 11 Pages.

We show how to use the GA concept of the ``rejection" of vectors, and also the related outer product, to derive equations for the location and radius of a triangle's incircle.
Category: Geometry

Algorithmic Computation of Multivector Inverses and Characteristic Polynomials in Non-Degenerate Clifford Algebras

Authors: Dimiter Prodanov
Comments: 9 Pages.

Clifford algebras provide the natural generalizations of complex, dual numbers and quaternions into the concept of non-commutative Clifford numbers.The paper demonstrates an algorithm for the computation of inverses of such numbers in a non-degenerate Clifford algebra of an arbitrary dimension.The algorithm is a variation of the Faddeev--LeVerrier--Souriau algorithm and is implemented in the open-source Computer Algebra System Maxima.Symbolic and numerical examples in different Clifford algebras are presented.
Category: Geometry