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Many areas of mathematics have a long history. For instance, calculus has been studied for hundreds of years. By contrast, courses on discrete structures emerged more recently during the past 50 years. They were designed to provide a mathematical support of computer science. Yet, bits and pieces of this subject have a longer history. We will begin with a playful recreational problem that fascinated Euler. The problem asks whether it is possible to move a knight on a chessboard such that it will visit each square of the chessboard precisely once. We will show that the question whether or not a solution exists depends on the size of the chessboard.

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Introduction

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  • 发表日期：

    2025年

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  • Andreas Klappenecker,
  • Hyunyoung Lee

摘要

Many areas of mathematics have a long history. For instance, calculus has been studied for hundreds of years. By contrast, courses on discrete structures emerged more recently during the past 50 years. They were designed to provide a mathematical support of computer science. Yet, bits and pieces of this subject have a longer history. We will begin with a playful recreational problem that fascinated Euler. The problem asks whether it is possible to move a knight on a chessboard such that it will visit each square of the chessboard precisely once. We will show that the question whether or not a solution exists depends on the size of the chessboard.