• Time Period: 800–500 BCE

• The Sulba Sutras, composed between 800 and 500 BCE, are ancient Indian mathematical treatises focusing on geometry.

• Location: Bharatvarsh

• The Sulba Sutras were utilized across the Indian subcontinent, showcasing the widespread influence of ancient Indian mathematical traditions. The geometric principles and mathematical concepts are outlined in specific chapters of the Sulba Sutras, such as the Baudhayan Sulba Sutra.

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• EVIDENCE:

1. Baudhayan Sulba Sutra, Chapter 1, Verse 12:

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परिकरण चतुरधिकं द्व्यांशे कृत्वोत्तरेणाथाऽनेकांशमिष्टाम्।

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MEANING: The rectangle of the diagonals is the sum of the squares on the sides.

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In this verse, Maharshi Baudhayan introduces a geometric principle related to a rectangle (aayat) and its diagonals. The sutra suggests that if we construct a rectangle and then form a square using the lengths of its two diagonals, the area of this square will be equal to the sum of the squares formed on the sides of the original rectangle.

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• For example, if you have a rectangle with sides of length 3 and 4 units, the diagonals would be 5 units each. According to this sutra, if you construct a square with a side length equal to the sum of the squares of the sides (3^2 + 4^2 = 9 + 16 = 25), it will be equivalent to the area formed by the diagonals.

 

• This geometric principle is an early example of the relationship between the sides and diagonals of rectangles, offering a mathematical understanding that could be applied in various geometric contexts. It reflects the mathematical sophistication of ancient Indian scholars in dealing with geometric concepts.

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2. Baudhayan Sulba Sutra, Chapter 2, Verse 10:

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दीर्घचतुरश्रस्याक्ष्णयारज्जुः पार्श्र्वमानी तिर्यग्विधानः।

यावदायामन्तरलोकस्तावद्वै योनो लोकः।

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MEANING: The diagonal of a rectangle is the rope stretched along the diagonal, which is made by the perpendicular and the horizontal sides. The result of this diagonal is the same as the square of the sum of the perpendicular and the base.

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In this verse, Maharshi Baudhayan has described the length of the diagonal of the rectangle. The outline of a rectangle is formed through perpendicular and adjacent straight lines of the base. According to the formula given in this verse, the length of the line (string) of the outline can be considered equal to the square of the sum of the vertex and the base.

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• Modern Science Connection: The Sulba Sutras, particularly the Baudhayan Sulba Sutra, contain geometric principles that foreshadow Modern Science concepts, especially in the field of geometry.

• For example: The Baudhayan sulba Sutra, includes discussions on the Pythagorean theorem and geometric constructions, showcasing advanced mathematical understanding in ancient India.