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Each row shows the state evolving until it repeats. The top row shows a generator with m = 9, a = 2, c = 0, and a seed of 1, which produces a cycle of length 6. The second row is the same generator with a seed of 3, which produces a cycle of length 2. Using a = 4 and c = 1 (bottom row) gives a cycle length of 9 with any seed in [0, 8].
The order of an element of a group (also called period length or period) is the order of the subgroup generated by the element. If the group operation is denoted as a multiplication , the order of an element a of a group, is thus the smallest positive integer m such that a m = e , where e denotes the identity element of the group, and a m ...
A prime p (where p ≠ 2, 5 when working in base 10) is called unique if there is no other prime q such that the period length of the decimal expansion of its reciprocal, 1/p, is equal to the period length of the reciprocal of q, 1/q. [8]
A function with period P will repeat on intervals of length P, and these intervals are sometimes also referred to as periods of the function. Geometrically, a periodic function can be defined as a function whose graph exhibits translational symmetry , i.e. a function f is periodic with period P if the graph of f is invariant under translation ...
In number theory, the nth Pisano period, written as π (n), is the period with which the sequence of Fibonacci numbers taken modulo n repeats. Pisano periods are named after Leonardo Pisano, better known as Fibonacci. The existence of periodic functions in Fibonacci numbers was noted by Joseph Louis Lagrange in 1774. [1] [2]
In particular, if n is any non-square positive integer, the regular continued fraction expansion of √ n contains a repeating block of length m, in which the first m − 1 partial denominators form a palindromic string.
The mean pregnancy length has been estimated to be 283.4 days of gestational age as timed from the first day of the last menstrual period and 280.6 days when retrospectively estimated by obstetric ultrasound measurement of the fetal biparietal diameter (BPD) in the second trimester. [12]
Diagram illustrating how the uterus lining builds up and breaks down during the menstrual cycle Menstruation (also known as a period, among other colloquial terms) is the regular discharge of blood and mucosal tissue from the inner lining of the uterus through the vagina. The menstrual cycle is characterized by the rise and fall of hormones. Menstruation is triggered by falling progesterone ...