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== '''[[Four color theorem]]''' ==
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<small>
The '''four color theorem''', sometimes known as the '''four color map theorem''' or '''Guthrie's problem''', is a [[problem]] in [[cartography]] and [[mathematics]]. It had been noticed that it only required four [[color]]s to fill in the different [[contiguous]] [[shape]]s on a [[map]] of regions or [[country|countries]] or [[province]]s in a flat surface known as a [[plane (geometry)|plane]] such that no two [[adjacent]] regions with a common [[boundary]] had the same color. But proving this [[proposition]] proved extraordinarily difficult, and it required [[analysis]] by high-powered [[computer]]s before the problem could be solved. In mathematical history, there had been numerous attempts to prove the supposition, but these so-called [[proof (mathematics)|proofs]] turned out to be flawed. There had been accepted proofs that a map could be colored in using more colors than four, such as six or five, but proving that only four colors were required was not done successfully until 1976 by mathematicians Appel and Haken, although some mathematicians do not accept it since parts of the proof consisted of an analysis of [[discrete]] cases by a computer.<ref name=Math1>{{cite news
==Footnotes==
|title= Four-Color Theorem
|publisher= Wolfram MathWorld
|quote= Six colors can be proven to suffice for the g=0 case, and this number can easily be reduced to five, but reducing the number of colors all the way to four proved very difficult. This result was finally obtained by Appel and Haken (1977), who constructed a computer-assisted proof that four colors were sufficient. However, because part of the proof consisted of an exhaustive analysis of many discrete cases by a computer, some mathematicians do not accept it. However, no flaws have yet been found, so the proof appears valid. A shorter, independent proof was constructed by Robertson et al. (1996; Thomas 1998).
|date= 2010-04-18
|url= http://mathworld.wolfram.com/Four-ColorTheorem.html
|accessdate= 2010-04-18
}}</ref> But, at the present time, the proof remains viable, and was confirmed independently by Robertson and Thomas in association with other mathematicians in 1996&ndash;1998 who have offered a simpler version of the proof, but it is still complex, even for advanced mathematicians.<ref name=Math1/> It is possible that an even simpler, more elegant, proof will someday be discovered, but many mathematicians think that a shorter, more elegant and simple proof is impossible.
 
''[[Four color theorem|.... (read more)]]''
 
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Latest revision as of 09:19, 11 September 2020

Paramhansa Yogananda circa 1920.

Paramhansa Yogananda (5 Jan 1893–7 Mar 1952) was one of the first Indian teachers from the Hindu spiritual tradition to reside permanently in the West, and in particular, he was the first to teach yoga to Americans. He emphasized the universality of the great religions, and ceaselessly taught that all religions, especially Hinduism and Christianity, were essentially the same in their essence. The primary message of Yogananda was to practice the scientific technique of kriya yoga to be released from all human suffering.

He emigrated from India to the United States in 1920 and eventually founded the Self-Realization Fellowship there in Los Angeles, California. He published his own life story in a book called Autobiography of a Yogi, first published in 1946. In the book, Yogananda provided some details of his personal life, an introduction to yoga, meditation, and philosophy, and accounts of his world travels and encounters with a wide variety of saints and colorful personalities, including Therese Neumann, Mohandas K. Gandhi, Luther Burbank, and Jagadis C. Bose.

Paramhamsa, also spelled Paramahamsa, is a Sanskrit title used for Hindu spiritual teachers who have become enlightened. The title of Paramhansa originates from the legend of the swan. The swan (hansa) is said to have a mythical ability to sip only the milk from a water-and-milk mixture, separating out the more watery part. The spiritual master is likewise said to be able to live in a world like a supreme (param) swan, and only see the divine, instead of all the evil mixed in there too, which the worldly person sees.

Yogananda is considered by his followers and many religious scholars to be a modern avatar.

In 1946, Yogananda published his Autobiography of a Yogi. It has since been translated into 45 languages, and in 1999 was designated one of the "100 Most Important Spiritual Books of the 20th Century" by a panel of spiritual authors convened by Philip Zaleski and HarperCollins publishers.

Awake: The Life of Yogananda is a 2014 documentary about Paramhansa Yogananda, in English with subtitles in seventeen languages. The documentary includes commentary by George Harrison and Ravi Shankar, among others.[1][2]

Footnotes
  1. ↑ Wikipedia has an article about the 2014 documentary film.
  2. ↑ The IMBd filmography database has a full cast list and other details about the 2014 documentary film.

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