Search results
Results From The WOW.Com Content Network
A simple fraction (also known as a common fraction or vulgar fraction) [n 1] is a rational number written as a/b or , where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include 1 / 2 , − 8 / 5 , −8 / 5 , and 8 / −5 .
For example, the repeating continued fraction [1;1,1,1,...] is the golden ratio, and the repeating continued fraction [1;2,2,2,...] is the square root of 2. In contrast, the decimal representations of quadratic irrationals are apparently random. The square roots of all (positive) integers that are not perfect squares are quadratic irrationals ...
The number π (/ p aɪ / ⓘ; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter.It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.
Profits from a joint fund. If two people put 200 and 100 into a fund and buy an ox for ploughing and use it for that purpose, they must divide the profit evenly between them. But if they instead slaughter the ox, the profit is divided proportionally. This is discussed in the Babylonian Talmud (just after the estate division problem). [4]
The Sulba Sutras give methods for constructing a circle with approximately the same area as a given square, which imply several different approximations of the value of π. [128] [129] [a] In addition, they compute the square root of 2 to several decimal places, list Pythagorean triples, and give a statement of the Pythagorean theorem. [129]
Sizes are often expressed as a fraction of an inch, with a one in the numerator, and a decimal number in the denominator. For example, 1/2.5 converts to 2/5 as a simple fraction , or 0.4 as a decimal number.
The 120-cell whose coordinates are given above of long radius √ 8 = 2 √ 2 ≈ 2.828 and edge-length 2 / φ 2 = 3− √ 5 ≈ 0.764 can be constructed in this manner just outside a 600-cell of long radius φ 2, which is smaller than √ 8 in the same ratio of ≈ 0.926; it is in the golden ratio to the edge length of the 600-cell ...