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Generalized Pentagonal Geometries-II
A generalized pentagonal geometry PENT( k , r , w ) is a partial linear space, where every line is incident with k points, every point is incident with r ...
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On the Floating Stability of Barges with Trapezoidal and Pentagonal Cross Sections
AbstractStability problems concerning the symmetrical equilibrium position for barges floating in a liquid, which have trapezoidal and pentagonal...
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Wave Propagation Characteristics of Thermoelastic Graphene Platelet Reinforced Polygonal Ring with Phase Lags
This article studies a new analytical method for clamped free generalized thermoelastic waves in a doubly connected polygonal ring reinforced with...
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Embedding World Series
During December 1991–January 1992, Paul Erdős and I were working on the book Problems of pgom Erdős at my home in Colorado Springs. Ron Graham called...
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Modeling of Delayed Thermo Elastic Waves in a Polygonal Ring Reinforced with Graphene Platelets
The free vibration analysis of generalized thermo elastic waves in a clamped free polygonal ring incorporated with graphene platelets is addressed in...
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TOND to TOND: Self-Similarity of Persian TOND Patterns, Through the Logic of the X-Tiles
Looking at the heritage of traditional Persian pentagonal patterns (patterns made from tiles derived from the pentagon), one can suppose that the...
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Allah’s Nonagons
A nonagon is a polygon with nine vertices on a circle and nine identical edges, but it cannot be drawn with a compass and ruler in a finite number of...
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The Tile-Maker Theorem and Its Applications to Art and Designs
Gen Hey, Kyuta! Can you search for artworks by Escher on the internet? Kyu OK. Will do…
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Curvature-Based r-Adaptive Isogeometric Analysis with Injectivity-Preserving Multi-Sided Domain Parameterization
Inspired by the r -refinement method in isogeometric analysis, in this paper, the authors propose a curvature-based r -adaptive isogeometric method for...
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Octagonal Layouts: Project Genesis of the Cathedral of Valencia
Octagonal layouts are widely used in medieval architecture. In Spain, the Cathedral of Valencia is an exceptional example because of its...
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Ancient Greek Big Bang Theory
From Plato to Kepler, some famous philosophers, scientists and alchemists using a remarkable blend of mathematics and faith try to explain the...
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Projective Geometry of Wachspress Coordinates
We show that there is a unique hypersurface of minimal degree passing through the non-faces of a polytope which is defined by a simple hyperplane...
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Stereotomy: Architecture and Mathematics
Stereotomy is the art of building with small structural elements, geometrically refined, which allow the construction of architectural systems with...
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Combinatorics Encoding Geometry: The Legacy of Bill Thurston in the Story of One Theorem
This chapter presents a whirlwind tour of some results surrounding the Koebe–Andre’ev–Thurston Theorem, Bill Thurston’s seminal circle packing...
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Group Operations
The first section deals with a special class of finite groups which have significance far beyond group theory: groups of permutations. In the two...
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Polyhedral Transformation Based on Confocal Quadratic Surface Properties. Graphical Speculations
Several procedures are presented that allow us to discretize a rotational quadratic surface in a simple way while fulfilling various geometric...
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More Than Three Coaxial Ellipsoids
The successful determination of the topology of three generic concentric ellipsoids runs into severe difficulties for more concentric ellipsoids,...
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Tri-simplicial Contradiction: The “Pascalian 3D Simplex” for the Oppositional Tri-segment
In this paper, we deal with the theory of the “oppositional poly-simplexes”, producing the first complete analysis of the simplest of them: the...