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108 (number)
108 (one hundred ndeight) is the natural number following 107 and preceding 109. In mathematics 108 is: *an abundant number. *a semiperfect number. *a tetranacci number. *the hyperfactorial of 3 since it is of the form 1^1 \cdot 2^2 \cdot 3^3. *divisible by the value of its φ function, which is 36. *divisible by the total number of its divisors (12), hence it is a refactorable number. *the angle in degrees of the interior angles of a regular pentagon in Euclidean space. *palindromic in bases 11 (9911), 17 (6617), 26 (4426), 35 (3335) and 53 (2253) *a Harshad number in bases 2, 3, 4, 6, 7, 9, 10, 11, 12, 13 and 16 *a self number. *an Achilles number because it is a powerful number but not a perfect power. *a largely composite number because its number of divisors is 12 and no smaller number has more than 12 divisors. *nine dozen, or three quarters of a gross. There are 108 free polyominoes of order 7. The equation 2\sin\left(\frac\right) = \phi results in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive integers Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers as well as zero. In other cases, the ''whole numbers'' refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary education, and are ambiguous as well although typically start at 1. The natural numbers are used for counting things, like "there are ''six'' coins on the table", in which case they are called ''cardinal numbers''. They are also used to put things in order, like "this is the ''third'' largest city in the country", which are called ''ordinal numbers''. Natural numbers are also used as labels, like Number (sports), jersey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Largely Composite Number
A highly composite number is a positive integer that has more divisors than all smaller positive integers. If ''d''(''n'') denotes the number of divisors of a positive integer ''n'', then a positive integer ''N'' is highly composite if ''d''(''N'') > ''d''(''n'') for all ''n'' < ''N''. For example, 6 is highly composite because ''d''(6)=4, and for ''n''=1,2,3,4,5, you get ''d''(''n'')=1,2,2,3,2, respectively, which are all less than 4. A related concept is that of a largely composite number, a positive integer that has at least as many divisors as all smaller positive integers. The name can be somewhat misleading, as the first two highly composite numbers (1 and 2) are not actually ; however, all further terms are. Ramanujan wrote a paper on high ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shaivism
Shaivism (, , ) is one of the major Hindu denominations, Hindu traditions, which worships Shiva as the Para Brahman, supreme being. It is the Hinduism#Demographics, second-largest Hindu sect after Vaishnavism, constituting about 385 million Hindus, found widely across South Asia (predominantly in South India, Southern India), Sri Lanka, and Nepal.Keay, p.xxvii. The followers of Shaivism are called Shaivas or Shaivites. According to Chakravarti, Shaivism developed as an amalgam of pre-Aryan religions and traditions, Vedic Rudra, and post-Vedic traditions, accommodating local traditions and Yoga, puja and bhakti. According to Bisschop, early shaivism is rooted in the worship of vedic deity Rudra. The earliest evidence for sectarian Rudra-Shiva worship appears with the Pasupata (early CE), possibly owing to the Origins of Hinduism, Hindu synthesis, when many local traditions were aligned with the Brahmanism, Vedic-Brahmanical fold. The Pāśupata movement rapidly expanded through ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gana
The word ( ) in Sanskrit and Pali means "flock, troop, multitude, number, tribe, category, series, or class". It can also be used to refer to a "body of attendants" and can refer to "a company, any assemblage or association of men formed for the attainment of the same aims". The word "gana" can also refer to councils or assemblies convened to discuss matters of religion or other topics. In Hinduism, the s are attendants of Shiva and live on Kailasha, Mount Kailash. Ganesha was chosen as their leader by Shiva; the deity's title is or , meaning, "lord or leader of the ". Literature Vedas The term gana is employed in the ''Rigveda'' in reference to the Maruts: Mahabharata Chapter 108 of the ''Shanti Parva'' of the ''Mahabharata'' describes a discussion between Yudhishthira and Bhishma regarding the strength of the ganas, how they defend themselves from disunion, the subjugation of their enemies, and forging friendships. Bhishma's answers to these questions are recorde ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mukhya
Principal Upanishads, also known as Mukhya Upanishads, are the most ancient and widely studied Upanishads of Hinduism. Composed between 800 BCE to the start of common era, these texts are connected to the Vedic tradition. Content The Principal Upanishads, which were composed probably between 600 and 300 BCE, constitute the concluding portion of the Veda. According to most Hindu traditions, ten Upanishads are considered as Principal Upanishads, but some scholars include , and into the list. The founders of the major schools of Vedanta, viz., Adi Shankara and Madhvacharya wrote (''commentaries'') on these ten Principal Upanishads. Even though Ramanuja did not write individual commentaries on Principal Upanishads, he quoted many hundreds of quotations from Upanishads in his Sri Bhasya. In the Ramanuja lineage, one of his followers, Rangaramanuja, wrote commentaries on almost all of the Principal Upanishads around the 1600s. The ten Principal Upanishads are: # (IsUp), Yajur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jainism
Jainism ( ), also known as Jain Dharma, is an Indian religions, Indian religion whose three main pillars are nonviolence (), asceticism (), and a rejection of all simplistic and one-sided views of truth and reality (). Jainism traces its spiritual ideas and history through the succession of twenty-four , supreme preachers of ''dharma''. The first in the current time cycle is Rishabhadeva, who tradition holds lived millions of years ago; the 23rd is Parshvanatha, traditionally dated to the 9th century Common Era, BCE; and the 24th is Mahāvīra, Mahavira, who lived . Jainism is considered an eternal ''dharma'' with the guiding every time cycle of the Jain cosmology, cosmology. Central to understanding Jain philosophy is the concept of ''bhedavijñāna'', or the clear distinction in the nature of the soul and non-soul entities. This principle underscores the innate purity and potential for liberation within every Jīva (Jainism), soul, distinct from the physical and menta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buddhism
Buddhism, also known as Buddhadharma and Dharmavinaya, is an Indian religion and List of philosophies, philosophical tradition based on Pre-sectarian Buddhism, teachings attributed to the Buddha, a wandering teacher who lived in the 6th or 5th century Before the Common Era, BCE. It is the Major religious groups, world's fourth-largest religion, with about 500 million followers, known as Buddhists, who comprise four percent of the global population. It arose in the eastern Gangetic plain as a movement in the 5th century BCE, and gradually spread throughout much of Asia. Buddhism has subsequently played a major role in Asian culture and spirituality, eventually spreading to Western world, the West in the 20th century. According to tradition, the Buddha instructed his followers in a path of bhavana, development which leads to Enlightenment in Buddhism, awakening and moksha, full liberation from ''Duḥkha, dukkha'' (). He regarded this path as a Middle Way between extremes su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hinduism
Hinduism () is an Hypernymy and hyponymy, umbrella term for a range of Indian religions, Indian List of religions and spiritual traditions#Indian religions, religious and spiritual traditions (Sampradaya, ''sampradaya''s) that are unified by adherence to the concept of ''dharma'', a Ṛta, cosmic order maintained by its followers through rituals and righteous living, as expounded in the Vedas. The word ''Hindu'' is an exonym, and while Hinduism has been called the oldest religion in the world, it has also been described by the modern term ''Sanātana Dharma'' () emphasizing its eternal nature. ''Vaidika Dharma'' () and ''Arya dharma'' are historical endonyms for Hinduism. Hinduism entails diverse systems of thought, marked by a range of shared Glossary of Hinduism terms, concepts that discuss God in Hinduism, theology, Hindu mythology, mythology, among other topics in Hindu texts, textual sources. Hindu texts have been classified into Śruti () and Smṛti (). The major Hin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dharmic Religions
Indian religions, sometimes also termed Dharmic religions or Indic religions, are the religions that originated in the Indian subcontinent. These religions, which include Buddhism, Hinduism, Jainism, and Sikhism,Adams, C. J."Classification of religions: Geographical"(), ''Encyclopædia Britannica'', 2007. Retrieved 15 July 2010. are also classified as Eastern religions. Although Indian religions are connected through the history of India, they constitute a wide range of religious communities, and are not confined to the Indian subcontinent. Evidence attesting to prehistoric religion in the Indian subcontinent derives from scattered Mesolithic rock paintings. The Harappan people of the Indus Valley civilisation, which lasted from 3300 to 1300 BCE (mature period 2600–1900 BCE), had an early urbanized culture which predates the Vedic religion. The documented history of Indian religions begins with the historical Vedic religion, the religious practices of the early Indo-Arya ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chord (trigonometry)
A chord (from the Latin ''chorda'', meaning "bowstring") of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord were to be extended Infinity, infinitely on both directions into a Line (geometry), line, the object is a ''secant line''. The perpendicular line passing through the chord's midpoint is called ''Sagitta (geometry), sagitta'' (Latin for "arrow"). More generally, a chord is a line segment joining two points on any curve, for instance, on an Ellipse#Chords, ellipse. A chord that passes through a circle's center point is the circle's ''diameter''. In circles Among properties of chords of a circle are the following: # Chords are equidistant from the center if and only if their lengths are equal. # Equal chords are subtended by equal angles from the center of the circle. # A chord that passes through the center of a circle is called a diameter and is the longest chord of that specific circle. # If the line extensions (secant lines) o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Golden Ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their summation, sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if \frac = \frac = \varphi, where the Greek letter Phi (letter), phi ( or ) denotes the golden ratio. The constant satisfies the quadratic equation and is an irrational number with a value of The golden ratio was called the extreme and mean ratio by Euclid, and the divine proportion by Luca Pacioli; it also goes by other names. Mathematicians have studied the golden ratio's properties since antiquity. It is the ratio of a regular pentagon's diagonal to its side and thus appears in the Straightedge and compass construction, construction of the dodecahedron and icosahedron. A golden rectangle—that is, a rectangle with an aspect ratio of —may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has bee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyomino
A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling. Polyominoes have been used in popular puzzles since at least 1907, and the enumeration of pentominoes is dated to antiquity. Many results with the pieces of 1 to 6 squares were first published in '' Fairy Chess Review'' between the years 1937 and 1957, under the name of "dissection problems." The name ''polyomino'' was invented by Solomon W. Golomb in 1953, and it was popularized by Martin Gardner in a November 1960 " Mathematical Games" column in ''Scientific American''. Related to polyominoes are polyiamonds, formed from equilateral triangles; polyhexes, formed from regular hexagons; and other plane polyforms. Polyominoes have been generalized to higher dimensions by joining cubes to form polycubes, or hypercubes to form polyhypercubes. In statistical physics, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
