no. 4
Diffusion des mathématiques, Histoire des mathématiques
On the construction of the Śrī Yantra
Chiodo, Alessandro1
1 Institut de Mathématiques de Jussieu — Paris Rive Gauche, Sorbonne Université, UMR 7586 C.N.R.S., 4 Pl. Jussieu,75252 Paris cedex, France
Comptes Rendus. Mathématique, Tome 359 (2021) no. 4, pp. 377-397.

Le śrīyantra (ou śrīcakra) est un diagramme sacré dans les traditions hindoues tantriques. Il a fait l’objet de nombreuses études dans différentes disciplines. En mathématiques, sa construction pose un problème élémentaire et non trivial. Dans cette note, on fournit une méthode de construction à la règle et au compas. La question est équivalente à celle d’un problème d’Apollonius qui consiste à trouver un cercle tangent à un cercle donné, à une droite donnée et passant par un point donné.

The Śrī Yantra (or Śrī Cakra) is a sacred diagram of Tantric Hinduism. Its study stimulated a vast effort of specialists from different fields. In mathematics, its construction sets an elementary and nontrivial problem. In this note, we work out a straightedge and compass method for constructing concurrent models of Śrī Yantras. The question is equivalent to the circle-line-point problem of Apollonious.

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DOI : 10.5802/crmath.163
Chiodo, Alessandro 1

1 Institut de Mathématiques de Jussieu — Paris Rive Gauche, Sorbonne Université, UMR 7586 C.N.R.S., 4 Pl. Jussieu,75252 Paris cedex, France 
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Chiodo, Alessandro. On the construction of the Śrī Yantra. Comptes Rendus. Mathématique, Tome 359 (2021) no. 4, pp. 377-397. doi : 10.5802/crmath.163. http://www.numdam.org/articles/10.5802/crmath.163/

[1] Bhowmik, Gautami Les carrés magiques de Nārāyaṇa, 2020 (published by CNRS Images des Mathématiques - La recherche mathématique en mots et en images, http://images.math.cnrs.fr/Les-carres-magiques-de-Nārāyaṇa.html)

[2] Bolton, Nicholas J.; Macleod, D. Nicol G. The geometry of the Śrīyantra, Religion, Volume 7 (1977) no. 1, pp. 66-85 | DOI

[3] de Casparis, J. G. Selected inscriptions from the 7th to the 9th century A. D., Bandung, Masa baru, 1956

[4] Eisenbud, David; Harris, Joe 3264 and All That: A Second Course in Algebraic Geometry, Cambridge University Press, 2016 | DOI | Zbl

[5] Fonseca, R. Constructive geometry of the Śrī-cakra diagram, Religion, Volume 16 (1986), pp. 33-49 | DOI

[6] Gupta, R. C. Yantras and mystic diagrams: a wild area of study for ancient and medieval Indian mathematics, Indian Journal of History of Science, Volume 42 (2007) no. 2, pp. 163-204 | Zbl

[7] Harris, Joe Theta-characteristics on algebraic curves, Trans. Am. Math. Soc., Volume 271 (1982) no. 2, pp. 611-638 | DOI | MR | Zbl

[8] Hartshorne, Robin Companion to Euclid, Berkeley Mathematics Lecture Notes, 9, American Mathematical Society, 1997

[9] Hartshorne, Robin Geometry: Euclid and Beyond, Undergraduate Texts in Mathematics, Springer, 2000 | DOI | Zbl

[10] Hohenwarter, Markus GeoGebra: Ein Softwaresystem für dynamische Geometrie und Algebra der Ebene, 2002 (Paris Lodron University, Salzburg, Austria, http://www.geogebra.org/)

[11] Huet, Gérard Śrī Yantra Geometry, Theor. Comput. Sci., Volume 281 (2002) no. 1-2, pp. 609-628 | DOI | MR | Zbl

[12] Jung, Carl Gustav Psychology of Yoga and Meditation: Lectures Delivered at ETH Zurich, Volume 6: 1938–1940, Philemon Foundation Series, Princeton University Press, 2020 (translated by John Peck and Heather McCartney, edited by Martin Liebscher)

[13] Kulaichev, Alexey Pavlovich Śrīyantra and its Mathematical Properties, Indian J. Hist. Sci., Volume 19 (1984) no. 3, pp. 279-292 | MR | Zbl

[14] Michaël, T. Le Śrīcakra dans la Saudrarya-Laharī, Mantras et diagrammes rituels dans l’Hindouisme (Padoux, Andre, ed.), CNRS Editions, 1986, pp. 127-139

[15] Mookerjee, Ajit; Khanna, Mahdu The Tantric Way, Thames and Hudson, London, 1977

[16] Navas, Andrés Le carré magique de Kharujaho est un hypercube (Images des Mathématiques), 2020 (with the collaboration of María José Moreno. Published by CNRS Images des Mathématiques - La recherche mathématique en mots et en images, http://images.math.cnrs.fr/Le-carre-magique-de-Kharujaho-est-un-hypercube.html)

[17] Padoux, Andre Le Cœur de la Yoginī — Yoginīhṛdaya, avec le commentaire Dīpikā d’Amaṛtānanda, Publications de l’Institut de Civilisation Indienne, Institut de civilisations Indienne (Collège de France) - Publications, 1994

[18] Pustynski, Vladislav-Veniamin On mathematical complexity of Śrīyantra, Indian Journal of History of Science, Volume 49 (2014) no. 3, pp. 268-277 | MR

[19] Ramachandra Rao, Saligrama Krishna The Yantras, Sri Garib Dass Oriental Series, 48, Sri Satguru Publications, 1988

[20] Rao, C. S. Śrīyantra — A study of spherical and plane forms, Indian Journal of History of Science, Volume 33 (1998) no. 3, pp. 203-227 | MR | Zbl

[21] Santhi, B.; Rajesh Kumar, N.; Bharathy, C.; Bala Krishnan, R. Generation of Divine Image–Sri Yantra, Research Journal of Applied Sciences, Engineering and Technology, Volume 4 (2012) no. 14, pp. 2241-2246

[22] Sastri, Pandit S. S.; Ayyangar, T. R. S. Saundarya Laharī, Theosophical Publishing House, 1948

[23] Tahta, Dick On the geometry of the sriyantra, The Mathematical Gazette, Volume 76 (1992) no. 475, pp. 49-60 | DOI

[24] Tularam, Gurudeo A. Investigating the Development of Arithmetic and Algebra in Vedic India, Tribute to Swami Dayananda Saraswati, International Journal of Mathematics, Game Theory and Algebra, Volume 20 (2012) no. 2, pp. 163-187 | MR | Zbl

[25] Wantzel, P. L. Recherches sur les moyens de reconnaître si un Problème de Géométrie peut se résoudre avec la règle et le compas, J. Math. Pures Appl., Volume 2 (1837), pp. 366-372

[26] Zimmer, Heinrich Artistic Form and Yoga in the Sacred Images of India, Princeton University Press, NJ, 1984 (trans. by G. Chapple, J. B. Lawson)

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