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Drawing with Complex Numbers [PDF]
The Mathematical Intelligencer, 2000 It is not commonly realized that the algebra of complex numbers can be used in an elegant way to represent the images of ordinary 3-dimensional figures, orthographically projected to the plane. We describe these ideas here, both using simple geometry and setting them in a broader context.
Michael Eastwood, Roger Penrose
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Applied Sciences, 2022 For dimensions two, three and four, we derive hyperbolic complex algebraic structures on the basis of suitably defined vector products and powers which allow in a standard way a series definitions of the hyperbolic vector exponential function.
Wolf-Dieter Richter
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Objects of categories as complex numbers [PDF]
Advances in Mathematics, 2004 In many everyday categories (sets, spaces, modules, ...) objects can be both added and multiplied. The arithmetic of such objects is a challenge because there is usually no subtraction. We prove a family of cases of the following principle: if an arithmetic statement about the objects can be proved by pretending that they are complex numbers, then ...
Marcelo Fiore, Tom Leinster
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On known and less known relations of Leonhard Euler with Poland [PDF]
Studia Historiae Scientiarum, 2016 In this work we focus on research contacts of Leonhard Euler with Polish scientists of his era, mainly with those from the city of Gdańsk (then Gedanum, Danzig). L.
Roman Sznajder
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Introduction to Third-Order Jacobsthal and Modified Third-Order Jacobsthal Hybrinomials
Discussiones Mathematicae - General Algebra and Applications, 2021 The hybrid numbers are generalization of complex, hyperbolic and dual numbers. In this paper, we introduce and study the third-order Jacobsthal and modified third-order Jacobsthal hybrinomials, i.e., polynomials, which are a generalization of the ...
Cerda-Morales Gamaliel
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Generalization of Neural Networks on Second-Order Hypercomplex Numbers
Mathematics, 2023 The vast majority of existing neural networks operate by rules set within the algebra of real numbers. However, as theoretical understanding of the fundamentals of neural networks and their practical applications grow stronger, new problems arise, which ...
Stanislav Pavlov +5 more
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On the Trigonometric and p-Trigonometric Functions of Elliptical Complex Variables
Communications in Advanced Mathematical Sciences, 2020 In the early 2000s, the geometry of a one-parameter family of generalized complex number systems was studied (Math. Mag. 77(2)(2004)). This family is denoted by Cp.
Kahraman Esen Özen
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Realism, irrationality, and spinor spaces
Zagadnienia Filozoficzne w Nauce, 2023 Mathematics, as Eugene Wigner noted, is unreasonably effective in physics. The argument of this paper is that the disproportionate attention that philosophers have paid to discrete structures such as the natural numbers, for which a nominalist ...
Adrian Heathcote
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Jacobsthal Representation Hybrinomials
Annales Mathematicae Silesianae, 2022 Jacobsthal numbers are a special case of numbers defined recursively by the second order linear relation and for these reasons they are also named as numbers of the Fibonacci type.
Liana Mirosław +2 more
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Global Registration of Terrestrial Laser Scanner Point Clouds Using Plane-to-Plane Correspondences
Remote Sensing, 2020 Registration of point clouds is a central problem in many mapping and monitoring applications, such as outdoor and indoor mapping, high-speed railway track inspection, heritage documentation, building information modeling, and others.
Nadisson Luis Pavan +2 more
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