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{"references": ["Ellis, E. V. (2015). Geomantic (Re) Creation: Magic Squares and Claude Bragdon's Theosophic Architecture. Architecture and Mathematics from Antiquity to the Future: Volume II: The 1500s to the Future, 289-303.", "Karpenko, V. (1994). Two thousand years of numerical magic squares. Endeavour, 18(4), 147-152.", "https://en.wikipedia.org/wiki/Magic_star", "http://recmath.org/Magic%20Squares/magicstar_def.htm", "Andrews, W. S. (1915). Magic Stars. The Monist, 25(1), 145-156", "Andrews, W. S. (1917). Magic squares and cubes. Open Court Publishing Company", "Ellis, E. V. (2001). Lo Shu, Window to the World of the Wondrous: Bragdon, Lissitzky, Malevich", "For\u00eat, P., & Kaplony, A. (Eds.). (2008). The journey of maps and images on the Silk Road (Vol. 21). Brill", "Tolsa, C. (2020). The earliest Arabic magic squares. Suhayl. International Journal for the History of the Exact and Natural Sciences in Islamic Civilisation, 7-24.", "Stapleton, H. E. (1953). The antiquity of alchemy. Ambix, 5(1-2), 1-43"]}
Much of alchemical knowledge will remain hidden forever. However, the written legacy that has reached us today continues to feed the imagination of historians, scientists and scholars around the world. It is this legacy that has allowed for the discovery of a magic star of order 5 composed of the numbers 1 to 9, repeating the number 5 only once. Despite the fact that there are no perfect order 5 stars, in the eyes of this author this solution is more perfect than existing solutions to date. Furthermore, a new construction method of pentagonal magic stars has been devised, based on magic squares of order 3. In honor of the work of the alchemists who inspired this discovery, we have named these stars Philosopher's Stars. In future works, the connection between magic squares and stars of higher orders will be explored in depth.
The author would like to acknowledge the insightful comments of Ms. Agata Gris Ergotiza.
magic star, recreational mathematics, alchemy, magic stars, pentagonal magic star, magic square, magic squares
magic star, recreational mathematics, alchemy, magic stars, pentagonal magic star, magic square, magic squares
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