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The latter fraction is the best possible rational approximation of π using fewer than five decimal digits in the numerator and denominator. Zu Chongzhi's results surpass the accuracy reached in Hellenistic mathematics, and would remain without improvement for close to a millennium.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
It is unknown whether these constants are transcendental in general, but Γ( 1 / 3 ) and Γ( 1 / 4 ) were shown to be transcendental by G. V. Chudnovsky. Γ( 1 / 4 ) / 4 √ π has also long been known to be transcendental, and Yuri Nesterenko proved in 1996 that Γ( 1 / 4 ), π, and e π are algebraically independent.
The mathematical constant e can be represented in a variety of ways as a real number.Since e is an irrational number (see proof that e is irrational), it cannot be represented as the quotient of two integers, but it can be represented as a continued fraction.
1/4 or 1 ⁄ 4 or ¼ may refer to: The calendar date January 4, in month-day format; The calendar date 1 April in day-month format; 1st Battalion, 4th Marines, an infantry battalion in the United States Marine Corps; A fraction of one fourth, one quarter, 25% or 0.25; 1/4 (single album), a single album by South Korean band Onewe
A unit fraction is a positive fraction with one as its numerator, 1/ n. It is the multiplicative inverse (reciprocal) of the denominator of the fraction, ...
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator p and a non-zero denominator q. [1] For example, 3 7 {\displaystyle {\tfrac {3}{7}}} is a rational number, as is every integer (for example, − 5 = − 5 1 {\displaystyle -5={\tfrac {-5}{1}}} ).
In the following quote, an "apertal ratio" of "1 ⁄ 24" is calculated as the ratio of 6 inches (150 mm) to 1 ⁄ 4 inch (6.4 mm), corresponding to an f /24 f-stop: In every lens there is, corresponding to a given apertal ratio (that is, the ratio of the diameter of the stop to the focal length), a certain distance of a near object from it ...