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In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form + + to the form + for some values of and . [1] In terms of a new quantity x − h {\displaystyle x-h} , this expression is a quadratic polynomial with no linear term.
He presented a method of completing the square to solve quadratic equations, sometimes called Śrīdhara's method or the Hindu method. Because the quadratic formula can be derived by completing the square for a generic quadratic equation with symbolic coefficients, it is called Śrīdharācārya's formula in some places.
As an example, the statement of circling the square is given in Baudhayana as: 2.9. 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 ...
Draw half its diagonal about the centre towards the East–West line; then describe a circle together with a third part of that which lies outside the square. Explanation: [ 9 ] Draw the half-diagonal of the square, which is larger than the half-side by x = a 2 2 − a 2 {\displaystyle x={a \over 2}{\sqrt {2}}-{a \over 2}} .
Unlike Abu'l-Hasan al-Uqlidisi's Kitab al-Fusul fi al-Hisab al-Hindi (The Arithmetics of Al-Uqlidisi) where the basic mathematical operation of addition, subtraction, multiplication and division were described in words, ibn Labban's book provided actual calculation procedures expressed in Hindu-Arabic numerals.
A sample of the Ashuri alphabet with tagin, written according to the Ashkenaz scribal custom on parchment (). Mention of the Ashuri script first appears in rabbinic writings of the Mishnaic and Talmudic periods, referring to the formal script used in certain Jewish ceremonial items, such as sifrei Torah, tefillin, mezuzot, and the Five Megillot.
This is also an application of completing the square, allowing us to write a quadratic polyomial of three variables in which all terms have degree two, as the sum of three squares. (My inspiration was a multivariate calculus problem: Create a tranformation to map the ellipsoid x 2 + 4 x y + 8 y 2 + 4 y z + 6 z 2 − 2 x z = 9 , {\displaystyle x ...
The area of a square is the product of the lengths of its sides. A square whose four sides have length has perimeter = and diagonal length =. (The square root of 2, appearing in this formula, is irrational, meaning that it is not the ratio of any two integers.