Related papers: Fun with Fonts: Algorithmic Typography
A characterization of real numbers constructible by paper folding.
We prove several hardness results on folding origami crease patterns. Flat-folding finite crease patterns is fixed-parameter tractable in the ply of the folded pattern (how many layers overlap at any point) and the treewidth of an…
Assembling parts into an object is a combinatorial problem that arises in a variety of contexts in the real world and involves numerous applications in science and engineering. Previous related work tackles limited cases with identical unit…
Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…
Typefaces are an essential resource employed by graphic designers. The increasing demand for innovative type design work increases the need for good technological means to assist the designer in the creation of a typeface. We present an…
Jigsaw puzzle solving requires the rearrangement of unordered pieces into their original pose in order to reconstruct a coherent whole, often an image, and is known to be an intractable problem. While the possible impact of automatic puzzle…
The goal of this article is to introduce some beautiful known riddles in intuitive topology; hoping to make at least some fun for the reader.
Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational…
Automatically creating a computer program using input-output examples can be a challenging task, especially when trying to synthesize computer programs that require loops or recursion. Even though the use of recursion can make the…
The theory of holographic algorithms, which are polynomial time algorithms for certain combinatorial counting problems, yields insight into the hierarchy of complexity classes. In particular, the theory produces algebraic tests for a…
A standard assumption in the study of logarithmic structures is "fineness", but this assumption is not preserved by intersections, fiber products, and more general limits. We explain how a coherent logarithmic scheme $X$ has a natural…
We introduce higher-dimensional cubical sliding puzzles that are inspired by the classical 15 Puzzle from the 1880s. In our puzzles, on a $d$-dimensional cube, a labeled token can be slid from one vertex to another if it is topologically…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
Origami describes rules for creating folded structures from patterns on a flat sheet, but does not prescribe how patterns can be designed to fit target shapes. Here, starting from the simplest periodic origami pattern that yields one…
We give a survey of algorithms for computing topological invariants of semi-algebraic sets with special emphasis on the more recent developments in designing algorithms for computing the Betti numbers of semi-algebraic sets. Aside from…
Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the problems discussed in this book will find…
In dependently typed programming, proofs of basic, structural properties can be embedded implicitly into programs and do not need to be written explicitly. Besides saving the effort of writing separate proofs, a most distinguishing and…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
We present new computational methods for proving diffeomorphy of triangulated 4-manifolds, including algorithms and topological software that can for the first time effectively handle the complexities that arise in dimension four and be…
We introduce a new type of programming challenge called programming puzzles, as an objective and comprehensive evaluation of program synthesis, and release an open-source dataset of Python Programming Puzzles (P3). Each puzzle is defined by…