Magic square (English Wikipedia)

Datta, Bibhutibhusan; Singh, Awadhesh Narayan (1992). "Magic Squares in India" (PDF). Indian Journal of History of Science. 27 (1): 51–120. Archived from the original (PDF) on 2018-01-17. Retrieved 2018-01-16.

archive.org

Andrews, William Symes (1917). Magic Squares and Cubes (2nd ed.). Open Court Publishing Company. p. 122.
Smith, David Eugene; Mikami, Yoshio (1914). A history of Japanese mathematics. Open Court Publishing Company. p. 69–75. Isomura Kittoku.
Smith, David Eugene; Mikami, Yoshio (1914). A history of Japanese mathematics. Open Court Publishing Company. p. 79–80. Isomura Kittoku.
Smith, David Eugene; Mikami, Yoshio (1914). A history of Japanese mathematics. Open Court Publishing Company. p. 116–122. Isomura Kittoku.
Smith, David Eugene; Mikami, Yoshio (1914). A history of Japanese mathematics. Open Court Publishing Company. p. 178. Isomura Kittoku.
Andrews, William Symes (1917). Magic Squares and Cubes (2nd ed.). Open Court Publishing Company. pp. 124–126.
Kraitchik, Maurice (1953). "Magic Squares". Mathematical Recreations (2nd ed.). New York: Dover Publications, Inc. pp. 142–192. ISBN 9780486201634.

arxiv.org

Pinn, K.; Wieczerkowski, C. (1998). "Number of Magic Squares From Parallel Tempering Monte Carlo". Int. J. Mod. Phys. C. 9 (4): 541. arXiv:cond-mat/9804109. Bibcode:1998IJMPC...9..541P. doi:10.1142/s0129183198000443. S2CID 14548422.
"Number of Magic Squares From Parallel Tempering Monte Carlo, arxiv.org, April 9, 1998. Retrieved November 2, 2013.

avclub.com

Zack Handlen (November 17, 2012). "The X-Files: "Biogenesis" / Millennium: "Goodbye To All That"". The A.V. Club. The Onion, Inc. Retrieved March 25, 2017. I love when they bring the nerdy FBI guy in to explain the concept of "the magic square", which he does by telling us that magic squares have been around for a while, and then nothing else. Unless I missed something, all I have at this point is that magic squares are squares that people once thought were magic.

books.google.com

Schwartzman, Steven (1994). The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English. MAA. p. 130.
Mikami, Yoshio (1917). Magic squares in Japanese mathematics (in Japanese). Tokyo: Imperial Academy of Science.
Needham, Joseph (1987). Theoretical Influences of China on Arabic Alchemy. UC Biblioteca Geral 1.
Stifel, Michael (1544), Arithmetica integra (in Latin), pp. 29–30.
Holger Vietor: Das Hexen-Einmaleins – der Weg zur Entschlüsselung. In: Goethe-Jahrbuch 122. Wallstein Verlag, Göttingen 2005, ISBN 3-8353-2195-1, S. 325–327 (German).

budshaw.ca

White, S. Harry. "Associative Magic Squares". budshaw.ca.
http://budshaw.ca/howMany.html, Bordered Square Numbers, S. Harry White, 2009
http://budshaw.ca/2xNComposite.html, 2N Composite Squares, S. Harry White, 2009

chinesehsc.org

Cammann, Schuyler (April 1960). "The Evolution of Magic Squares in China" (PDF). Journal of the American Oriental Society. 80 (2): 116–124. doi:10.2307/595587. JSTOR 595587.

core.ac.uk

The Influence of Chinese Mathematical Arts on Seki Kowa by Shigeru Jochi, MA, School of Oriental and African Studies, University of London, 1993
Hayashi, Takao (1987). "Varahamihira's Pandiagonal Magic Square of the Order Four" (PDF). Historia Mathematica. 14 (2): 159–166. doi:10.1016/0315-0860(87)90019-X.

doi.org

Yoke, Ho Peng (2008). "Magic Squares in China". Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Encyopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures (2 ed.). Springer. pp. 1252–1259. doi:10.1007/978-1-4020-4425-0_9350. ISBN 978-1-4020-4559-2.
Cammann, Schuyler (April 1960). "The Evolution of Magic Squares in China" (PDF). Journal of the American Oriental Society. 80 (2): 116–124. doi:10.2307/595587. JSTOR 595587.
Michiwaki, Yoshimasa (2008). "Magic Squares in Japanese Mathematics". Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Encyopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures (2 ed.). Springer. pp. 1252–1259. doi:10.1007/978-1-4020-4425-0_9154. ISBN 978-1-4020-4559-2.
Hayashi, Takao (2008). "Magic Squares in Indian Mathematics". Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures (2 ed.). Springer. pp. 1252–1259. doi:10.1007/978-1-4020-4425-0_9778. ISBN 978-1-4020-4559-2.
Hayashi, Takao (1987). "Varahamihira's Pandiagonal Magic Square of the Order Four" (PDF). Historia Mathematica. 14 (2): 159–166. doi:10.1016/0315-0860(87)90019-X.
Sesiano, Jacques (November 2003). "Construction of magic squares using the knight's move in Islamic mathematics" (PDF). Archive for History of Exact Sciences. 58 (1): 1–20. doi:10.1007/s00407-003-0071-4. S2CID 123219466.
Cammann, Schuyler (February 1969). "Islamic and Indian Magic Squares, Part I". History of Religions. 8 (3): 181–209. doi:10.1086/462584. S2CID 162095408.
Cammann, Schuyler (May 1969). "Islamic and Indian Magic Squares, part II". History of Religions. 8 (4): 271–299. doi:10.1086/462589. JSTOR 1062018. S2CID 224806255.
Boyer, Christian (12 November 2008). "Some Notes on the Magic Squares of Squares Problem". The Mathematical Intelligencer. 27 (2): 52–64. doi:10.1007/BF02985794.
Loly, Peter (March 2004) [1 August 2016]. "The invariance of the moment of inertia of magic squares" (PDF). Mathematical Gazette. 88 (511): 151–153. CiteSeerX 10.1.1.552.7296. doi:10.1017/S002555720017456X. S2CID 125989925. Archived from the original (PDF) on 14 November 2017. Retrieved 5 June 2017.
Marcus, M.; Ree, R. (1959). "Diagonals of doubly stochastic matrices". The Quarterly Journal of Mathematics. 10 (1): 296–302. doi:10.1093/qmath/10.1.296.
Pinn, K.; Wieczerkowski, C. (1998). "Number of Magic Squares From Parallel Tempering Monte Carlo". Int. J. Mod. Phys. C. 9 (4): 541. arXiv:cond-mat/9804109. Bibcode:1998IJMPC...9..541P. doi:10.1142/s0129183198000443. S2CID 14548422.
Kitajima, Akimasa; Kikuchi, Macoto; Altmann, Eduardo G. (14 May 2015). "Numerous but Rare: An Exploration of Magic Squares". PLOS ONE. 10 (5): e0125062. Bibcode:2015PLoSO..1025062K. doi:10.1371/journal.pone.0125062. PMC 4431883. PMID 25973764.
Sallows, Lee (Fall 1997) [9 January 2009]. "The lost theorem". The Mathematical Intelligencer. 19 (4): 51–54. doi:10.1007/BF03024415. S2CID 122385051.

dr-mikes-math-games-for-kids.com

Hartley, M. "Making Big Magic Squares".

futilitycloset.com

"Area Magic Squares". Futility Closet. 2017-01-19. Retrieved 2017-06-12.

harvard.edu

ui.adsabs.harvard.edu

Pinn, K.; Wieczerkowski, C. (1998). "Number of Magic Squares From Parallel Tempering Monte Carlo". Int. J. Mod. Phys. C. 9 (4): 541. arXiv:cond-mat/9804109. Bibcode:1998IJMPC...9..541P. doi:10.1142/s0129183198000443. S2CID 14548422.
Kitajima, Akimasa; Kikuchi, Macoto; Altmann, Eduardo G. (14 May 2015). "Numerous but Rare: An Exploration of Magic Squares". PLOS ONE. 10 (5): e0125062. Bibcode:2015PLoSO..1025062K. doi:10.1371/journal.pone.0125062. PMC 4431883. PMID 25973764.

helsinki.fi

helda.helsinki.fi

Muurinen, Ismo (2020). Fermat, magic squares and the idea of self-supporting blocks (PDF) (MSc). University of Helsinki.

holycross.edu

mathcs.holycross.edu

Gareth E. Roberts (March 23, 2015). "Composing with Numbers: Sir Peter Maxwell Davies and Magic Squares" (PDF). Retrieved December 25, 2018.

jstor.org

Cammann, Schuyler (April 1960). "The Evolution of Magic Squares in China" (PDF). Journal of the American Oriental Society. 80 (2): 116–124. doi:10.2307/595587. JSTOR 595587.
Cammann, Schuyler (May 1969). "Islamic and Indian Magic Squares, part II". History of Religions. 8 (4): 271–299. doi:10.1086/462589. JSTOR 1062018. S2CID 224806255.

law05.si

http://www.law05.si/iwms/presentations/Styan.pdf Some illustrated comments on 5×5 golden magic matrices and on 5×5 Stifelsche Quadrate, George P. H. Styan, 2014.

littlereview.com

Michelle Erica Green (June 15, 1997). "Biogenesis on The X-Files". littlereview.com. The Little Review. Retrieved March 25, 2017. Moreover, it's a magic square, a pattern in which God supposedly instructed the early Hebrews to gain power from names or their numeric equivalents.

maa.org

"The Magic Squares of Manuel Moschopoulos - Introduction | Mathematical Association of America". www.maa.org.

macaupost.gov.mo

Macau Post Office web site Archived 2014-11-11 at the Wayback Machine

markfarrar.co.uk

Karl Fulves, Self-working Number Magic (Dover Magic Books)

mathforum.org

Adler, Allan; Alejandre, Suzanne. "Why there are no 2x2 magic squares". mathforum.org. Archived from the original on 2018-03-02.

maths.org

plus.maths.org

Anything but square: from magic squares to Sudoku by Hardeep Aiden, Plus Magazine, March 1, 2006

nrich.maths.org

Hawley, Del (2011). "Magic Squares II". nrich.maths.org. University of Cambridge.

muljadi.org

"Virtual Home of Paul Muljadi". Archived from the original on 2005-11-09. Retrieved 2005-03-18.

multimagie.com

"Multimagie.com – Additive-Multiplicative magic squares, 8th and 9th-order". Retrieved 26 August 2015.
"Multimagie.com – Smallest additive-multiplicative magic square". Retrieved 16 January 2024.

nih.gov

ncbi.nlm.nih.gov

Kitajima, Akimasa; Kikuchi, Macoto; Altmann, Eduardo G. (14 May 2015). "Numerous but Rare: An Exploration of Magic Squares". PLOS ONE. 10 (5): e0125062. Bibcode:2015PLoSO..1025062K. doi:10.1371/journal.pone.0125062. PMC 4431883. PMID 25973764.

pubmed.ncbi.nlm.nih.gov

Kitajima, Akimasa; Kikuchi, Macoto; Altmann, Eduardo G. (14 May 2015). "Numerous but Rare: An Exploration of Magic Squares". PLOS ONE. 10 (5): e0125062. Bibcode:2015PLoSO..1025062K. doi:10.1371/journal.pone.0125062. PMC 4431883. PMID 25973764.

nsta.org

static.nsta.org

Gardner, Martin (January 1996). "The magic of 3x3" (PDF). Quantum. 6 (3): 24–26. ISSN 1048-8820. Retrieved 6 January 2024.
Gardner, Martin (March 1996). "The latest magic" (PDF). Quantum. 6 (4): 60. ISSN 1048-8820. Retrieved 6 January 2024.

nthu.edu.tw

oz.nthu.edu.tw

http://oz.nthu.edu.tw/~u9621110/IT2010/txt/0929/canterburypuzzle00dudeuoft.pdf The Canterbury Puzzles and Other Curious Problems, Henry Ernest Dudeney, 1907

pourlascience.fr

Les carrés magiques géométriques by Jean-Paul Delahaye, Pour La Science No. 428, June 2013

psu.edu

citeseerx.ist.psu.edu

Loly, Peter (March 2004) [1 August 2016]. "The invariance of the moment of inertia of magic squares" (PDF). Mathematical Gazette. 88 (511): 151–153. CiteSeerX 10.1.1.552.7296. doi:10.1017/S002555720017456X. S2CID 125989925. Archived from the original (PDF) on 14 November 2017. Retrieved 5 June 2017.

rero.ch

doc.rero.ch

Sesiano, Jacques (November 2003). "Construction of magic squares using the knight's move in Islamic mathematics" (PDF). Archive for History of Exact Sciences. 58 (1): 1–20. doi:10.1007/s00407-003-0071-4. S2CID 123219466.

sagradafamilia.org

blog.sagradafamilia.org

"The magic square on the Passion façade: keys to understanding it". 7 February 2018.

semanticscholar.org

api.semanticscholar.org

Sesiano, Jacques (November 2003). "Construction of magic squares using the knight's move in Islamic mathematics" (PDF). Archive for History of Exact Sciences. 58 (1): 1–20. doi:10.1007/s00407-003-0071-4. S2CID 123219466.
Cammann, Schuyler (February 1969). "Islamic and Indian Magic Squares, Part I". History of Religions. 8 (3): 181–209. doi:10.1086/462584. S2CID 162095408.
Cammann, Schuyler (May 1969). "Islamic and Indian Magic Squares, part II". History of Religions. 8 (4): 271–299. doi:10.1086/462589. JSTOR 1062018. S2CID 224806255.
Loly, Peter (March 2004) [1 August 2016]. "The invariance of the moment of inertia of magic squares" (PDF). Mathematical Gazette. 88 (511): 151–153. CiteSeerX 10.1.1.552.7296. doi:10.1017/S002555720017456X. S2CID 125989925. Archived from the original (PDF) on 14 November 2017. Retrieved 5 June 2017.
Pinn, K.; Wieczerkowski, C. (1998). "Number of Magic Squares From Parallel Tempering Monte Carlo". Int. J. Mod. Phys. C. 9 (4): 541. arXiv:cond-mat/9804109. Bibcode:1998IJMPC...9..541P. doi:10.1142/s0129183198000443. S2CID 14548422.
Sallows, Lee (Fall 1997) [9 January 2009]. "The lost theorem". The Mathematical Intelligencer. 19 (4): 51–54. doi:10.1007/BF03024415. S2CID 122385051.

sites.google.com

"Magic cube with Dürer's square" Ali Skalli's magic squares and magic cubes
Skalli, Ali (14 October 2009). "Magic cube with Gaudi's square". Archived from the original on 15 December 2021.
"8x8 multiplicative magic square of complex numbers" Ali Skalli's magic squares and magic cubes

st-and.ac.uk

www-groups.dcs.st-and.ac.uk

O'Connor, J.J.; Robertson, E.F. "Yang Hui". MacTutor History of Mathematics Archive. Retrieved 15 March 2018.

st-andrews.ac.uk

www-history.mcs.st-andrews.ac.uk

O'Connor, J.J.; Robertson, E.F. "Benjamin Franklin". MacTutor History of Mathematics Archive. Retrieved 15 December 2018.

theguardian.com

Magic squares are given a whole new dimension, The Observer, April 3, 2011
Macau's magic square stamps just made philately even more nerdy The Guardian Science, November 3, 2014

tripod.com

jeff560.tripod.com

Miller, Jeff (September 3, 2016). "Earlier Known Uses of Some of the Words of Mathematics (M)".

trump.de

How many magic squares are there? by Walter Trump, Nürnberg, January 11, 2001

umanitoba.ca

home.cc.umanitoba.ca

Loly, Peter (March 2004) [1 August 2016]. "The invariance of the moment of inertia of magic squares" (PDF). Mathematical Gazette. 88 (511): 151–153. CiteSeerX 10.1.1.552.7296. doi:10.1017/S002555720017456X. S2CID 125989925. Archived from the original (PDF) on 14 November 2017. Retrieved 5 June 2017.

uriland.it

This manuscript text (circa 1496–1508) is also at the Biblioteca Universitaria in Bologna. It can be seen in full at the address http://www.uriland.it/matematica/DeViribus/Presentazione.html Archived 2012-03-01 at the Wayback Machine

web.archive.org

Datta, Bibhutibhusan; Singh, Awadhesh Narayan (1992). "Magic Squares in India" (PDF). Indian Journal of History of Science. 27 (1): 51–120. Archived from the original (PDF) on 2018-01-17. Retrieved 2018-01-16.
This manuscript text (circa 1496–1508) is also at the Biblioteca Universitaria in Bologna. It can be seen in full at the address http://www.uriland.it/matematica/DeViribus/Presentazione.html Archived 2012-03-01 at the Wayback Machine
"Virtual Home of Paul Muljadi". Archived from the original on 2005-11-09. Retrieved 2005-03-18.
Skalli, Ali (14 October 2009). "Magic cube with Gaudi's square". Archived from the original on 15 December 2021.
Adler, Allan; Alejandre, Suzanne. "Why there are no 2x2 magic squares". mathforum.org. Archived from the original on 2018-03-02.
Loly, Peter (March 2004) [1 August 2016]. "The invariance of the moment of inertia of magic squares" (PDF). Mathematical Gazette. 88 (511): 151–153. CiteSeerX 10.1.1.552.7296. doi:10.1017/S002555720017456X. S2CID 125989925. Archived from the original (PDF) on 14 November 2017. Retrieved 5 June 2017.
Macau Post Office web site Archived 2014-11-11 at the Wayback Machine

wolfram.com

mathworld.wolfram.com

Wolfram MathWorld: Magic Square Weisstein, Eric W.
"MathWorld News: There Are No Magic Knight's Tours on the Chessboard".

worldcat.org

Gardner, Martin (January 1996). "The magic of 3x3" (PDF). Quantum. 6 (3): 24–26. ISSN 1048-8820. Retrieved 6 January 2024.
Gardner, Martin (March 1996). "The latest magic" (PDF). Quantum. 6 (4): 60. ISSN 1048-8820. Retrieved 6 January 2024.