Sulbasutra

The Sulbasutras ("string rules" or "guide to the art of measuring") are Indian records from the middle of the first millennium BC. BC ( Vedic Period ). They contain geometrical rules for the construction of altars. Of these three have been preserved:

• Baudhayana Sulbasutra (about 600 to 500 BC)
• Apastamba Sulbasutra (about 500 to 400 BC)
• Katyayana Sulbasutra (about 400 to 300 BC)

These three scriptures have essentially the same content. In them the construction of right angles can be found with the help of right triangles , the side lengths of which are Pythagorean triples (for example 3, 4, 5 and 5, 12, 13). The transformation of a rectangle into a square of equal area can also be found there. As an approximation for the value of the root 2 is

${\displaystyle 1+{\frac {1}{3}}+{\frac {1}{4}}\cdot {\frac {1}{3}}-{\frac {1}{34}}\cdot {\frac {1}{4\cdot 3}}}$

specified.

Figures (straight lines, circles) are drawn with a rope (rajju, sulba) and fixed points (posts), the sanku. The most important problems related to the drawing of squares, right angles, parallels, trapezoids and rectangles and an important motif the surface of a geometric figure, as they arose from the religiously motivated demand to construct altars in different shapes with the same area. Accordingly, the highlight of their representation is the geometric transformation of figures (circles, squares, rectangles, isosceles triangles, rhombuses and trapezoids ) with the same surface area. They contain the oldest literal rendering of the Pythagorean theorem (which was already known in ancient Babylonia), in identical word wording in all three Sulbasutras: The diagonal cord (aksnaya-rajju) of a rectangle creates both the flank (parsvamani) and the Create horizontal (tiryanmani) separately .

literature

• Helmuth Gericke : Mathematics in Antiquity, Orient and Occident. Marix Verlag, Wiesbaden 2005, ISBN 3-937715-71-1 , pp. 66-69.
• SN Sen, AK Bag: The Sulbasutras of Baudhayana, Apastamba, Katyayana, ´and Manava. Indian National Science Academy, New Delhi 1983.
• AK Bag: Geometry in Ancient and Medieval India. New Delhi, 1979.
• Jean-Michel Delire: Un chapitre du Baudhayana Sulbasutra. Traduction et commentaires concernant les connaissances mathématiques de l'Inde védique. Mémoire, Philologie et Histoire Orientales, Université Libre de Bruxelles 1993.
• Olivier Keller: Préhistoire de la géométrie: la gestation d'une science d'après les sources archéologiques et ethnographiques. Thèse, Histoire et civilizations (Histoire des sciences), École des Hautes Études en Sciences Sociales, Paris 1998.
• BB Datta : The Science of the Sulba. Calcutta 1932.

Web links

• JJ O'Connor, EF Robertson: The Indian Sulbasutras. (November 2000)
• Olivier Keller, La geometry des Sulbasutras, IREM No. 40, July 2000, pdf, French

Individual evidence

1. ↑ Takao Hayashi: Indian Mathematics, in: Gavin Flood, The Blackwell Companion to Hinduism, Blackwell 2003, p. 363