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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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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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Classical Greek and Roman Architecture: Mathematical Theories and Concepts
In classical antiquity only round numbers — natural integers — were known, and mathematics was very different to the way it is today. But whereas the...
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Computer Experiment in Teaching Mathematics
AbstractA mathematical experiment has always been a key source for a mathematical discovery. Over the past 50 years, thanks to digital technologies,...
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Odd or Even, Jitterbug Versus Grünbaum’s Double Polyhedra
Coxeter, Longuet-Higgins & Miller (Coxeter et al. Uniform polyhedra. Philosophical Transactions of the Royal Society London 401–450, 1954) define...
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Completely Solving the Quintic by Iteration
In the late nineteenth century, Felix Klein revived the problem of solving the quintic equation from the moribund state into which Galois had placed...
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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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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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Synthetic Methods for Constructing Polyhedra
In this paper, we propose an explanation and application of the synthetic method to the representation of the Platonic and Archimedean Solids (PS and...
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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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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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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 module theory of semisymmetric quasigroups, totally symmetric quasigroups, and triple systems
This paper initiates a unified module theory for four varieties of quasigroups: semisymmetric, semisymmetric idempotent, totally symmetric, and...
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Pentagonal Structures as Impulse for Art
The work of the contemporary Dutch artist Gerard Caris is presented as an example, how art creations and design processes can follow a strong...
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Tailoring via Sculpting
In this chapter we complete the proof that one slice of P by plane Π can be tailored to the face of Q lying in Π, following the sequence...
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Filling Space with Gyroid Symmetry
The gyroid is a triply periodic minimal surface that belongs to the associate family of the Schwarz P and D surfaces, and has several point...
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Scientific Sources and Representations of the Small Stellated Dodecahedra Painted in Genoa
The present study investigates the history, significance, and depiction of a polyhedron painted in the Room of Leda, as part of the decorative plan...