Related papers: Fun with Fonts: Algorithmic Typography
One presents many Concatenated and Operation Sequences, P-Q Relationships, Digital Sequences, Magic Squares, Prime Conjectures, k-Divisibility and Strong Divisibility Sequences, Geometric Conjectures, Proposed problems.
Typology is a subfield of linguistics that focuses on the study and classification of languages based on their structural features. Unlike genealogical classification, which examines the historical relationships between languages, typology…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
We present and discuss seven different open problems in applied combinatorics. The application areas relevant to this compilation include quantum computing, algorithmic differentiation, topological data analysis, iterative methods,…
The hypercomputers compute functions or numbers, or more generally solve problems or carry out tasks, that cannot be computed or solved by a Turing machine. Several numerical simulations of a possible hypercomputational algorithm based on…
You can invent striking and challenging problems with unique solution by building some symmetry into functional equations. Some are suitable for high school; others could generate college-level projects involving computer algebra. The…
We consider so-called squaring the square-puzzles where a given square (or rectangle) should be dissected into smaller squares. For a specific instance of such problems we demonstrate that a mathematically rigorous solution can be quite…
Can folding a piece of paper flat make it larger? We explore whether a shape $S$ must be scaled to cover a flat-folded copy of itself. We consider both single folds and arbitrary folds (continuous piecewise isometries $S\rightarrow R^2$).…
We design new visual illusions by finding "adversarial examples" for principled models of human perception -- specifically, for probabilistic models, which treat vision as Bayesian inference. To perform this search efficiently, we design a…
One of the most significant problems in cuneiform pedagogy is the process of looking up unknown signs, which often involves a tedious page-by-page search through a sign list. This paper proposes a new "recursive encoding" for signs, which…
Quantum graphs have become in this century a favorite playground for mathematicians, mathematical physicists, and chemists, due to their manifold applications as models of thin structures, as well as presenting sometimes simpler playground…
Kirigami tessellations, regular planar patterns formed by cutting flat, thin sheets, have attracted recent scientific interest for their rich geometries, surprising material properties and promise for technologies. Here we pose and solve…
As the second book in the Anyone Can Code series, Algorithmic Thinking focuses on the logic behind computer programming and software design. With a data-centred approach, it starts with simple algorithms that work on simple data items and…
Origami is an ancient art that continues to yield both artistic and scientific insights to this day. In 2012, Buhler, Butler, de Launey, and Graham extended these ideas even further by developing a mathematical construction inspired by…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
Many programming problems call for turning geometrical thoughts into code: tables, hierarchical structures, nests of objects, trees, forests, graphs, and so on. Linear text does not do justice to such thoughts. But, it has been the dominant…
This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite geometries, simple groups, sphere packings,…
This paper introduces the problem of automatic font pairing. Font pairing is an important design task that is difficult for novices. Given a font selection for one part of a document (e.g., header), our goal is to recommend a font to be…
The Art Gallery Problem is one of the most well-known problems in Computational Geometry, with a rich history in the study of algorithms, complexity, and variants. Recently there has been a surge in experimental work on the problem. In this…
We briefly introduce several problems: (1) a generalization of the convex fair partition conjecture, (2) on non-trivial invariants among polyhedrons that can be formed from the same set of face polygons, (3) two questions on assembling…