Related papers: Automated Generation of Triangle Geometry Theorems

Automatic generation of level maps is a popular form of automatic content generation. In this study, a recently developed technique employing the {\em do what's possible} representation is used to create open-ended level maps. Generation of…

In this paper, we provide methods to automatically obtain automata that generate polyominoes inscribed in a rectangle of fixed width and increasing height. We use them to obtain the generating function of those sequences for small widths.

Recent studies show increasing demands and interests in automatically generating layouts, while there is still much room for improving the plausibility and robustness. In this paper, we present a data-driven layout framework without model…

Causal loop and stock and flow diagrams are broadly used in System Dynamics because they help organize relationships and convey meaning. Using the analytical work of Schoenberg (2019) to select what to include in a compressed model, this…

To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an…

We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient…

We describe some theoretical results on triangulations of surfaces and we develop a theory on roots, decompositions and genus-surfaces. We apply this theory to describe an algorithm to list all triangulations of closed surfaces with at most…

We show upper and lower bounds for angles in iterations of trisections of certain triangulations.

We introduce a bulging triangle like the generalization of the Reuleaux triangle. We may be able to propose various ways to bulge a triangle, but this paper presents the way so that its vertices are the same as them of the original…

We propose a new geometric method of IR factorization in sector decomposition. The problem is converted into a set of problems in convex geometry. The latter problems are solved using algorithms in combinatorial geometry. This method…

A triangulation of a surface is irreducible if there is no edge whose contraction produces another triangulation of the surface. In this work we propose an algorithm that constructs the set of irreducible triangulations of any surface with…

Most learners fail to develop deep text comprehension when reading textbooks passively. Posing questions about what learners have read is a well-established way of fostering their text comprehension. However, many textbooks lack…

We consider the problem of graph generation guided by network statistics, i.e., the generation of graphs which have given values of various numerical measures that characterize networks, such as the clustering coefficient and the number of…

We provide a novel approach to construct generative models for graphs. Instead of using the traditional probabilistic models or deep generative models, we propose to instead find an algorithm that generates the data. We achieve this using…

In this note we prove that elementary maps on triangular algebras are automically additive.

Automated insight generation is a common tactic for helping knowledge workers, such as data scientists, to quickly understand the potential value of new and unfamiliar data. Unfortunately, automated insights produced by large-language…

The concept of a morphism determined by an object provides a method to construct or classify morphisms in a fixed category. We show that this works particularly well for triangulated categories having Serre duality. Another application of…

One of the most promising developments in computer vision in recent years is the use of generative neural networks for functionality condition-based 3D design reconstruction and generation. Here, neural networks learn dependencies between…

In this paper, we explore a new approach for automated chess commentary generation, which aims to generate chess commentary texts in different categories (e.g., description, comparison, planning, etc.). We introduce a neural chess engine…

(Shortened version of abstract in article itself) This article describes an algorithm for producing, for any desired resolution and any desired numbers of wheel and pinion teeth, polygonal approximations to the shapes of a pair of cycloidal…