This is correct (when rounded) to 2 decimal places. Pythagorus. (c – BC). Theorem. (c. 8th century BCE) composed. Baudhayana Sulba Sutra., the best-. BAUDHAYANA (PYTHAGORAS) THEOREM It was ancient Indians been provided by both Baudhāyana and Āpastamba in the Sulba Sutras!. It was known in the Sulbasutra (for example, Sutra 52 of Baudhayana’s Sulbasutram) that the diagonal of a square is the side of another square with two times.
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The Shulba Sutras are part of the larger corpus of texts called the Shrauta Baudhzyanaconsidered to be appendices to the Vedas. They are the only sources of knowledge of Indian mathematics from the Vedic period.
Unique fire-altar shapes were associated with unique gifts from the Gods. For instance, “he who desires heaven is to construct a fire-altar in the form of a falcon”; “a fire-altar in the form of a tortoise is to be constructed by one desiring to win the world of Brahman” and “those who wish to destroy existing and future enemies should construct a fire-altar in the form of a rhombus”. The four major Shulba Sutras, which are mathematically the most significant, are those attributed to BaudhayanaManavaApastamba and Katyayana.
The sutras contain discussion and non-axiomatic demonstrations of cases of the Pythagorean theorem and Pythagorean triples. In Baudhayana, the rules are given as follows:. The diagonal of a square produces double the area [of the square].
The areas [of the squares] produced separately by the lengths of the breadth of a rectangle together equal the area [of the square] produced by the diagonal. This is observed in rectangles having sides 3 and 4, 12 and 5, 15 and 8, 7 and 24, 12 and 35, 15 and The Satapatha Brahmana and the Taittiriya Samhita were probably also aware of the Pythagoras theorem.
Staal illustrates an application of the Pythagorean Theorem in the Shulba Sutra to convert a rectangle to a square of equal area. Apastamba ‘s rules for building right angles in altars use the following Pythagorean triples: The same triples are easily derived from an old Babylonian rule, which makes Mesopotamian influence on the sutras likely. The Baudhayana Shulba sutra gives the construction of geometric shapes such as squares and rectangles.
These include transforming a square into a rectanglean isosceles trapeziuman isosceles trianglea rhombusand a circleand transforming a circle into a square.
As an example, the statement of circling the square is given in Baudhayana as:. If it is desired to transform a square into a circle, [a cord of length] half the diagonal [of the square] is stretched from the centre to the east [a part of it lying outside the eastern side of the square]; with one-third [of the part lying outside] added to the remainder [of the half diagonal], the [required] circle is drawn.
To transform a circle into a square, the diameter is divided into eight parts; one [such] part after being divided into twenty-nine baudhayanaa is reduced by twenty-eight of them and further by the sixth [of the part left] less the eighth [of the sixth part]. Alternatively, divide [the diameter] into fifteen parts and reduce it by two of them; this gives the approximate side of the square [desired]. The constructions in 2. Altar construction also led to an estimation of the baushayana root of 2 as found in three of the sutras.
In the Baudhayana sutra it appears as:. The measure is to be increased by its third and this [third] again by its own fourth less the thirty-fourth part [of that fourth]; this is [the value of] the diagonal of a square [whose side is the measure].
This formula is similar in structure to the formula found on a Mesopotamian tablet  from the Old Babylonian period BCE: Indeed, an early method for calculating square roots can be found in some Sutras, the method involves the recursive formula: Before the period of the Stra was at an end, the Brahmi numerals had definitely begun to appear c. More importantly even still was the development of the concept of decimal place value.
It has also been suggested the sutras contain the concept of incommensurability. From Wikipedia, the free encyclopedia. Part of a series on Hinduism Hindu History Concepts.
Certain shapes and sizes of fire-altars were associated with particular gifts that the sacrificer desired from the gods: A History of Mathematics 2nd ed. We find rules for the construction of right angles by baudhayanq of triples of cords the lengths of which form Pythagorean triages, such as 3, 4, and 5, or 5, 12, and 13, or 8, 15, and 17, or 12, 35, and However all of these triads are easily derived from the old Babylonian rule; hence, Mesopotamian influence in the Sulvasutras is not unlikely.
Aspastamba knew that the square on the diagonal of a rectangle is equal to the sum of the squares on the two adjacent sides, but this form of the Pythagorean theorem also may have been derived from Bsudhayana. So conjectural are the origin and period of the Sulbasutras that we cannot tell whether or not the rules are related to early Egyptian surveying or to the later Greek problem of altar doubling. They are variously dated within an interval of almost a thousand years stretching from the eighth century B.
The Crest of the Peacock: The Non-European Roots of Mathematics. The “circulature” and quadrature techniques in 2.
Shulba Sutras – Wikipedia
The Hindus had a very good system of approximating irrational square roots. This approximation follows a rule given by the twelfth century Muslim mathematician Al-Hassar. Walter Eugene Clark David Pingree. Babylonian mathematics Chinese mathematics Greek mathematics Islamic mathematics European mathematics.
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Area of a circle Circumference Use in other formulae.