Islamic and Indian Magic Squares I

Suhayl

My aim here is to shed light on the origins of magic squares in the Islamic world. This question has often been tentatively addressed, but previous studies have considered only part of the evidence. The earliest Arabic texts presenting squares (al-Ṭabarī, Jābir ibn Ḥayyān, Ghāyat al-Ḥakīm, Brethren of Purity) are examined here together for the first time, as well as the Indian medical sources. The extraordinary coincidences in the use of the square of three in therapy for a good delivery in both the early Arabic texts and the Indian, as well as the close cultural, geographical, and chronological context, strongly suggests that such eutocic practice represents the origin of Islamic magic squares.

Encyclopaedia of Islam, 2023

Magic squares A magic square is called in Arabic a wafq (harmony, agreement) or wafq al-add (harmonious disposition of numbers), and ilm al-awfq is the study of such squares; occasionally the more general term for any tabular presentation, jadwal, was used (Günther and Pielow; Hallum).

Historia Mathematica, 1987

Muqarnas, Supplements, Volume: 14, 2019

Gülru Necipoğlu, Cemal Kafadar and Cornell H. Fleischer (eds.), Treasures of Knowledge: An Inventory of the Ottoman Palace Library (1502/3-1503/4) (2 vols) (Leiden: Brill, 2019), 341–366.

2018

Future Vision, 2003

An intriguing example of Square Kufic style of Arabic calligraphy was executed for King Pedero I in his palace Alcazar in Seville, Spain, in 1364. Muslim artisans used blue and white ceramic tiles to form a decorative panel over the entrance facade to the courtyard. The geometric panel contained many crosses, which must have pleased the Christian patron, but was in fact composed of the phrase “There is no victor but God,” the slogan of the Nasrid rulers of Granada at the time, the city where these Muslim craftsmen came from to execute this project.

This essay shows all the most important numbers associated with the 7 magick squares of Cornelius Agrippa, along with others, can be found on an extended ordinal counting sequence version of the Tetractys of Pythagoras. That is by counting out numbers in a triangular form the "triangular numbers" are highlighted in the pattern and this also shows the numbers of magick squares. A detailed look at this numerical Tetractys is given, with interpretations on what it could mean for Pythagoras, the Kabbalistic cube of space, along with cubic numbers and even the Sri Yantra and Chakra systems. (Showing Kabbalistic numbers in the Sri Yantra) Building upon the work of David Fideler and his book "Jesus Christ Sun of God" gematria is used to interpret the biblical parables of 153 fish and the feeding of 5000. All this shows how magick squares and their associated numerology is the basis for various traditions of number mysticism. While there is far more to explore in terms of interpreting texts, with the evidence provided, the main thesis shows how the magick squares undeniably fit with the Tetractys and that Polygonal numbers in general are also very important.

Aestimatio: Sources and Studies in the History of Science

The two earliest Arabic treatises explaining the construction of magic squares date from the 10th century ad. One is found in the Commentary on the Arithmetical [Introduction] (Kitāb tafsīr al-Arithmāṭīqī) by ʿAlī ibn Aḥmad al-Anṭākī (d. 376 H/ad 987). Only book 3 of the original three books is extant, and that in a single manuscript. This book is divided into three chapters: the first is a collection of arithmetical definitions, statements of propositions, and identities assembled from Greek and Arabic sources; the second is on magic squares; and the third deals with “hidden numbers”, in which a person thinks of a number and another discovers it after operations are performed on it. Curiously, none of these chapters have anything to do with Nicomachus’ Arithmetical Introduction, on which the book is supposed to be a commentary. Reviewed by: Jeffrey A. Oaks Published Online (2022-07-31)Copyright © 2022 by Jeffrey A. Oaks Article PDF Link: https://jps.library.utoronto.ca/index.php/ae...