相关论文: Similarity of Triangles and Intercept Theorem in E…

This article studies the systems of equations appearing in the Susa Mathematical Texts (\textbf{SMT}) and the different approaches used by the Susa scribes to solve them.

In this article, we study some of quadratic equations and their solutions found in the Susa Mathematical Texts (\textbf{SMT}). We show that the Susa scribes used this group of equations in different problems and took a standard approach,…

This article studies the application of the Pythagorean theorem in the Susa Mathematical Texts (\textbf{SMT}) and we discuss those texts whose problems and related calculations demonstrate its use. Among these texts, \textbf{SMT No.\,1}…

In this article, we study a particular group of plane figures whose constants are listed in the Susa Mathematical Tablet No.\,3 (\textbf{SMT No.\,3}). We explain possible ways to define these figures and seek to demonstrate that the Susa…

This article studies three-dimensional objects and their volumes in Elamite mathematics, particularly those found in the Susa Mathematical Tablet No.\,14 (\textbf{SMT No.\,14}). In our discussion, we identify some basic solids whose volumes…

In this article, we study the problems found in the Susa Mathematical Texts No.\,24 and No.\,25 (\textbf{SMT No.\,24} and \textbf{SMT No.\,25}) which concern excavation projects such as canals and holes. We also examine certain Elamite…

In this paper, a theorem about similar triangles is proved. It shows that two small and four large triangles similar to the original triangle can appear if we choose well among several intersections of the perpendicular bisectors of the…

In this paper we first study the isoperimetric problem in the case of integer triangles, as well as Alcuin's sequence and how it relates to the number of different integer triangles with a given perimeter. We then present and compare two…

The bisection of trapezoids by transversal lines has many examples in Babylonian mathematics. In this article, we study a similar problem in Elamite mathematics, inscribed on a clay tablet held in the collection of the Louvre Museum and…

Semantic Textual Similarity (STS) is the basis of many applications in Natural Language Processing (NLP). Our system combines convolution and recurrent neural networks to measure the semantic similarity of sentences. It uses a convolution…

In this paper the problem of finding a normal form of triangles and plane quadrilaterals up to similarity is considered. Several normal forms for triangles and a normal form for quadrilaterals of special case are described. Normal forms of…

In this article, we study the inscription on the reverse of Susa Mathematical Text No.\,2, a clay tablet held in the collection of the Louvre Museum and thought to date from between 1894--1595 BC. We focus on the formula given in this text…

We study equivalence relation of the set of triangles generated by similarity and operation on a triangle to get a new one by joining division points of three edges with the same ratio. Using the moduli space of similarity classes of…

While there has been substantial progress in learning suitable distance metrics, these techniques in general lack transparency and decision reasoning, i.e., explaining why the input set of images is similar or dissimilar. In this work, we…

Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is a theorem of A. Pitts, which shows that uniform interpolation holds for intuitionistic…

We revisit the algorithmic problem of finding a triangle in a graph (\textsc{Triangle Detection}), and examine its relation to other problems such as \textsc{3Sum}, \textsc{Independent Set}, and \textsc{Graph Coloring}. We obtain several…

We present a, hopefully, elementary mathematical treatment of the computational aspects of congruent numbers, such that an amateur could understand the problem and perform their own calculations.

Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…

Text embeddings are a fundamental component in many NLP tasks, including classification, regression, clustering, and semantic search. However, despite their ubiquitous application, challenges persist in interpreting embeddings and…

The goal of our industrial ticketing system is to retrieve a relevant solution for an input query, by matching with historical tickets stored in knowledge base. A query is comprised of subject and description, while a historical ticket…