Clifford Algebra to Geometric Calculus. A Unified Language for Mathematics and Physics

1985 ◽  
Vol 53 (5) ◽  
pp. 510-511 ◽  
Author(s):  
David Hestenes ◽  
Garret Sobczyk ◽  
James S. Marsh
Keyword(s):  
Clifford Algebra ◽  
Geometric Calculus ◽  
Mathematics And Physics

Clifford Algebra to Geometric Calculus

1985 ◽  
Vol 69 (448) ◽  
pp. 158
Author(s):  
C. W. Kilmister ◽  
D. Hestenes ◽  
G. Sobczyk
Keyword(s):  
Clifford Algebra ◽  
Geometric Calculus

scholarly journals Some Applications of Clifford Algebra in Geometry

2020 ◽  
Author(s):  
Ying-Qiu Gu
Keyword(s):  
Clifford Algebra ◽  
Simple Calculation ◽  
Riemann Geometry ◽  
Geometric Concepts ◽  
Vector Algebra ◽  
Complex Quaternion ◽  
Concise Representation ◽  
Definition Of ◽  
Mathematics And Physics ◽  
Area And Volume

In this paper, we provide some enlightening examples of the application of Clifford algebra in geometry, which show the concise representation, simple calculation and profound insight of this algebra. The definition of Clifford algebra implies geometric concepts such as vector, length, angle, area and volume, and unifies the calculus of scalar, spinor, vector and tensor, so that it is able to naturally describe all variables and calculus in geometry and physics. Clifford algebra unifies and generalizes real number, complex, quaternion and vector algebra, converts complicated relations and operations into intuitive matrix algebra independent of coordinate systems. By localizing the basis or frame of space-time and introducing differential and connection operators, Clifford algebra also contains Riemann geometry. Clifford algebra provides a unified, standard, elegant and open language and tools for numerous complicated mathematical and physical theories. Clifford algebra calculus is an arithmetic-like operation that can be well understood by everyone. This feature is very useful for teaching purposes, and popularizing Clifford algebra in high schools and universities will greatly improve the efficiency of students to learn fundamental knowledge of mathematics and physics. So Clifford algebra can be expected to complete a new big synthesis of scientific knowledge.

Clifford Algebra to Geometric Calculus

1984 ◽  
Author(s):  
David Hestenes ◽  
Garret Sobczyk
Keyword(s):  
Clifford Algebra ◽  
Geometric Calculus

Birds and frogs in mathematics and physics

2010 ◽  
Vol 180 (8) ◽  
pp. 859 ◽  
Author(s):  
F. Dyson
Keyword(s):  
Mathematics And Physics

Ingenious Mathematical Insights

2019 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
New Type ◽  
Mathematics And Physics

The purpose of this paper is to introduce a new type of microarticle, considered for publishing in the Open Journal of Mathematics and Physics (OJMP), dubbed "Mathematical Insight."

Series expansions for monogenic functions in Clifford algebras and their application

2020 ◽  
Vol 17 (3) ◽  
pp. 365-371
Author(s):  
Anatoliy Pogorui ◽  
Tamila Kolomiiets
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Space ◽  
Clifford Algebra ◽  
Clifford Algebras ◽  
Monogenic Function ◽  
Second Order ◽  
Series Expansions ◽  
Monogenic Functions ◽  
Partial Differential

This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.

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