Drawing with Complex Numbers
Michael Eastwood,Roger Penrose +1 more
21
TL;DR: In this paper, 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, both using simple geometry and setting them in a broader context.
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Abstract: 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.
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Citations
•Posted Content
A class of quadratic difference equations on a finite graph
TL;DR: In this paper, a class of complex polynomial equations on a finite graph with a view to understanding how holistic phenomena emerge from combinatorial structure was studied, namely dimension, distance and curvature.
4
Constant mean curvature polytopes and hypersurfaces via projections
TL;DR: In this paper, it was shown that a smooth version of the quadratic difference equation is satisfied independently of the projection, where the parameter ρ depends only on the mean curvature.
3
Orthogonal projections of cubes and regular simplices into a plane
TL;DR: In this article, it was shown that for every k ≥ 2 and k ≥ k, there is a unit cube of unit edge which is mapped to a regular 2k-gon by an orthogonal projection onto a subspace.
2
•Posted Content
Quadratic Cyclic Sequences.
TL;DR: In this article, relations between cyclic sequences determined by a quadratic difference relation, cyclotomic polynomials, Eulerian digraphs and walks in the plane are explored.
1
References
A Generalized inverse for matrices
Roger Penrose
- 01 Jul 1955
TL;DR: A generalization of the inverse of a non-singular matrix is described in this paper as the unique solution of a certain set of equations, which is used here for solving linear matrix equations, and for finding an expression for the principal idempotent elements of a matrix.
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Geometry and the imagination
David Hilbert,Stefan Cohn-Vossen +1 more
- 01 Jan 1952
TL;DR: The simplest curves and surfaces Regular systems of points Projective configurations Differential geometry Kinematics Topology Index as mentioned in this paper The simplest curve and surface regular system of points projective configurations Projective configuration
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•Book
Engineering drawing and geometry
Randolph P. Hoelscher,Clifford Harry Springer +1 more
- 01 Jan 1961
14