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And the other three binary-expansion repeating sequences give the 3-cycle 110110110... → 101101101... → 011011011... → 110110110.... Either of these 3-cycles can be converted to fraction form: for example, the first-given 3-cycle can be written as 1 / 7 → 2 / 7 → 4 / 7 → 1 / 7 .
The base "Roman fraction" is S, indicating 1 ⁄ 2. The use of S (as in VIIS to indicate 7 1 ⁄ 2 ) is attested in some ancient inscriptions [ 45 ] and also in the now rare apothecaries' system (usually in the form SS ): [ 44 ] but while Roman numerals for whole numbers are essentially decimal , S does not correspond to 5 ⁄ 10 , as one might ...
The convergents of the continued fraction for φ are ratios of successive Fibonacci numbers: φ n = F n+1 / F n is the n-th convergent, and the (n + 1)-st convergent can be found from the recurrence relation φ n+1 = 1 + 1 / φ n. [31] The matrix formed from successive convergents of any continued fraction has a determinant of +1 or −1.
Jesus The Christ Pantocrator of Saint Catherine's Monastery at Mount Sinai, 6th century AD Born c. 6 to 4 BC [a] Herodian kingdom, Roman Empire Died AD 30 or 33 (aged 33 or 38) Jerusalem, Judaea, Roman Empire Cause of death Crucifixion [b] Known for Central figure of Christianity Major prophet in Islam and in Druze Faith Manifestation of God in Baháʼí Faith Parent(s) Mary, Joseph [c] Jesus ...
The Lidov–Kozai resonance can significantly alter the orbits of these moons: for example, the eccentricity and inclination of the group's namesake Carpo can fluctuate between 0.19–0.69 and 44–59°, respectively. [37] Valetudo is the outermost prograde moon and is not part of a known family. Its prograde orbit crosses paths with several ...
This is an accepted version of this page This is the latest accepted revision, reviewed on 13 February 2025. Gas in an atmosphere with certain absorption characteristics This article is about the physical properties of greenhouse gases. For how human activities are adding to greenhouse gases, see Greenhouse gas emissions. Greenhouse gases trap some of the heat that results when sunlight heats ...
The Pareto principle may apply to fundraising, i.e. 20% of the donors contributing towards 80% of the total. The Pareto principle (also known as the 80/20 rule, the law of the vital few and the principle of factor sparsity [1] [2]) states that for many outcomes, roughly 80% of consequences come from 20% of causes (the "vital few").
Claude is a family of large language models developed by Anthropic. [1] [2] The first model was released in March 2023.The Claude 3 family, released in March 2024, consists of three models: Haiku optimized for speed, Sonnet balancing capabilities and performance, and Opus designed for complex reasoning tasks.