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The Swadhyaya Movement or Swadhyaya Parivara started in mid 20th-century in the western states of India, particularly Maharashtra and Gujarat. [1] Founded by Pandurang Shastri Athavale (1920-2003), the movement emphasizes self-study (swadhyaya), selfless devotion and application of Indian scriptures such as the Upanishads and Bhagavad gita for spiritual, social and economic liberation.
This view is shared by Baudhayana Dharmasastra in verses 4.1.29 to 4.1.30, which adds that ‘‘svadhyaya is a means of getting past one’s past mistakes and any guilt”. [34] Baudhayana Dharmasastra describes ‘‘Svadhyaya’’, in verse 2.6.11, as the path to Brahman (Highest Reality, Universal Spirit, Eternal Self).
In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...
Rational number arithmetic is the branch of arithmetic that deals with the manipulation of numbers that can be expressed as a ratio of two integers. [93] Most arithmetic operations on rational numbers can be calculated by performing a series of integer arithmetic operations on the numerators and the denominators of the involved numbers.
Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.
Dhanashree Talwalkar is the daughter and spiritual heir of Pandurang Shastri Athavale (Dadaji), a philosopher, social scientist, and founder of the Swadhyay (pronounced ‘swaadhyaay’) Parivar (meaning family). She is the leader of “Silent but Singing” Swadhyay movement. At the age of 20, she conducted the first “Geetatrayah” – a ...
This group is always finite. The ring of integers possesses unique factorization if and only if it is a principal ring or, equivalently, if has class number 1. Given a number field, the class number is often difficult to compute. The class number problem, going back to Gauss, is concerned with the existence of imaginary quadratic number fields ...
Namely, Lehmer showed that for relatively prime integers k and n with n > 2, the number 2 cos(2πk/n) is an algebraic number of degree φ(n)/2, where φ denotes Euler's totient function. Because rational numbers have degree 1, we must have n ≤ 2 or φ(n) = 2 and therefore the only possibilities are n = 1,2,3,4,6.