Scholarlink

<p>Magic squares, particularly the 4 × 4 pandiagonal (PD) ones, offer a distinct allure because of the property that rows, columns, principal diagonals, as well as all the broken diagonals, give the magic sum. Building on our earlier exploration of Nārāyaṇa Paṇḍita’s horse-move (<i>turagagati</i>) method, and drawing in particular on additional properties identified in a recent study, this paper presents a simple four-step procedure for constructing PD magic squares within a novel quadrilayered framework. In this method, we begin with four arbitrary numbers {a,b,c,d}, and from them generate the entire PD magic square in just four steps. Additionally, we also find that the characteristic polynomial satisfied by such a square (considering it as a matrix) takes a much simpler and elegant form than the one that is available in the literature.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A simple 4-step method for constructing \(4\times 4\) pandiagonal magic squares

  • 期刊论文

  • 发表日期：

    2026年3月1日

查看全文
  • Varuneshwar Reddy Mandadi,
  • D G Sooryanarayan,
  • K Ramasubramanian

摘要

Magic squares, particularly the 4 × 4 pandiagonal (PD) ones, offer a distinct allure because of the property that rows, columns, principal diagonals, as well as all the broken diagonals, give the magic sum. Building on our earlier exploration of Nārāyaṇa Paṇḍita’s horse-move (turagagati) method, and drawing in particular on additional properties identified in a recent study, this paper presents a simple four-step procedure for constructing PD magic squares within a novel quadrilayered framework. In this method, we begin with four arbitrary numbers {a,b,c,d}, and from them generate the entire PD magic square in just four steps. Additionally, we also find that the characteristic polynomial satisfied by such a square (considering it as a matrix) takes a much simpler and elegant form than the one that is available in the literature.