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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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Geometric and Aesthetic Concepts Based on Pentagonal Structures
The relationship between geometry and art will be examined using the example of pentagonal structures. The work of contemporary Dutch artist Gerard...
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Geometry and Proportions in Anne Tyng’s Architecture
Anne Tyng spent her long professional life devoted to architecture, mainly in its theoretical aspects linked with geometry and proportions. She is...
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On the Logical Geometry of Geometric Angles
In this paper we provide an analysis of the logical relations within the conceptual or lexical field of angles in 2D geometry. The basic tripartition...
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Geometry and Topology
This chapter presents a collection of theorems in geometry and topology, proved in the twenty-first, which are at the same time great and easy to...
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Geometric and Aesthetic Concepts Based on Pentagonal Structures
The relationship between geometry and art will be examined using the example of pentagonal structures. The work of contemporary Dutch artist Gerard...
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Geometric and Aesthetic Concepts Based on Pentagonal Structures
The relationship between geometry and art will be examined using the example of pentagonal structures. The work of contemporary Dutch artist Gerard...
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Non-Uniform Polyhedra Described by Daniele Barbaro
In La Terza Parte of the treatise La pratica della perspettiva, published in 1568, Daniele Barbaro describes 39 solid bodies between Chapters I and...
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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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On a Class of Polyhedra with Symmetrical Vertex Stars
The influence of the local symmetry of stars of some vertices of a closed convex polyhedron in E 3 on its geometry is considered. A theorem on the...
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The Regular Polyhedra: Drawing and Computing in Euclid’s day
Can we compute what we cannot draw? How must we draw to produce measurable representations, or visual ones? This research inquires into the...
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Art from Tiling Patterns
Gen Hi, Kyuta. You look bored. Kyu Oh, Gen. What kind of mathematical topics will you tell me about today?
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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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Introduction
The problem of covering a flat surface — a subset of the Euclidean plane or the whole plane itself — using some fixed geometric shapes and with no...
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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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Doing Mathematics with 3D Pens: Five Years of Research on 3D Printing Integration in Mathematics Classrooms
Technology has the transformative potential to induce deep changes in thinking, learning, and doing mathematics. In this chapter, we discuss the...
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The Dome as Minimal Housing Unit: “Ghibli” and “D-Home” Prototypes
In this paper are presented two domed minimal housing units: Ghibli and D-Home. Both prototypes were outlined from the discretization of a domed...