Search results
Results from the WOW.Com Content Network
The spiral is started with an isosceles right triangle, with each leg having unit length.Another right triangle (which is the only automedian right triangle) is formed, with one leg being the hypotenuse of the prior right triangle (with length the square root of 2) and the other leg having length of 1; the length of the hypotenuse of this second right triangle is the square root of 3.
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Donate
The Babylonian clay tablet YBC 7289 (c. 1800–1600 BC) gives an approximation of the square root of 2 in four sexagesimal figures, 𒐕 𒌋𒌋𒐼 𒐐𒐕 𒌋 = 1;24,51,10, [13] which is accurate to about six decimal digits, [14] and is the closest possible three-place sexagesimal representation of √ 2:
Inverting this process allows square roots to be found, and similarly for the powers 3, 1/3, 2/3, and 3/2. Care must be taken when the base, x, is found in more than one place on its scale. For instance, there are two nines on the A scale; to find the square root of nine, use the first one; the second one gives the square root of 90.
(A quadratic field consists of all numbers of the form +, where and are rational numbers and is a fixed rational number whose square root is not rational.) For that matter, the eleventh-century chakravala method amounts—in modern terms—to an algorithm for finding the units of a real quadratic number field.
The topics treated include arithmetic (fractions, square roots, profit and loss, simple interest, the rule of three, and regula falsi) and algebra (simultaneous linear equations and quadratic equations), and arithmetic progressions. In addition, there is a handful of geometric problems (including problems about volumes of irregular solids).
The square root of a positive integer is the product of the roots of its prime factors, because the square root of a product is the product of the square roots of the factors. Since p 2 k = p k , {\textstyle {\sqrt {p^{2k}}}=p^{k},} only roots of those primes having an odd power in the factorization are necessary.
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}} .