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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.
In mathematics, a Cauchy sequence is a sequence whose elements become arbitrarily close to each other as the sequence progresses. [1] More precisely, given any small positive distance, all excluding a finite number of elements of the sequence are less than that given distance from each other.
Generalization to fractions is by multiplying the numerators and denominators, respectively: = (). This gives the area of a rectangle A B {\displaystyle {\frac {A}{B}}} high and C D {\displaystyle {\frac {C}{D}}} wide, and is the same as the number of things in an array when the rational numbers happen to be whole numbers.
Nicolas Chuquet used a form of exponential notation in the 15th century, for example 12 2 to represent 12x 2. [11] This was later used by Henricus Grammateus and Michael Stifel in the 16th century. In the late 16th century, Jost Bürgi would use Roman numerals for exponents in a way similar to that of Chuquet, for example iii 4 for 4 x 3 .
However, this relaxed form of Egyptian fractions does not allow for any number to be represented using fewer fractions, as any expansion with repeated fractions can be converted to an Egyptian fraction of equal or smaller length by repeated application of the replacement + = + + (+) if k is odd, or simply by replacing 1 / k + 1 / k ...
There's no general answer; it depends on the liquid (in particular its refractive index), what material the lens is made out of, the exact form of the lens (e.g. radius of curvature of each surface), and the distance between the lens and the mirror.