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The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares.It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, [1] and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. [2]
Most numbers have a unique quater-imaginary representation, but just as 1 has the two representations 1 = 0. 9 in decimal notation, so, because of 0. 0001 2i = 1 / 15 , the number 1 / 5 has the two quater-imaginary representations 0. 0003 2i = 3· 1 / 15 = 1 / 5 = 1 + 3· –4 / 15 = 1. 0300 2i.
An imaginary number is the product of a real number and the imaginary unit i, [note 1] which is defined by its property i 2 = −1. [1] [2] The square of an imaginary number bi is −b 2. For example, 5i is an imaginary number, and its square is −25. The number zero is considered to be both real and imaginary. [3]
If these potential digit-sums are used in the formula 2 x digit-sum x 11, the digit-sum of the result will determine whether or not the result is an Osiris number. 1. 2 x 6 x 11 = 132. 2. Digit-sum (132) = 1 + 2 + 3 = 6. 3. Therefore 132 is an Osiris number. 1. 2 x 7 x 11 = 154. 2. Digit-sum (154) = 1 + 5 + 4 = 10. 3. Therefore 154 is not an ...
r = | z | = √ x 2 + y 2 is the magnitude of z and; φ = arg z = atan2(y, x). φ is the argument of z, i.e., the angle between the x axis and the vector z measured counterclockwise in radians, which is defined up to addition of 2π. Many texts write φ = tan −1 y / x instead of φ = atan2(y, x), but the first equation needs ...
0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, ... "subtract if possible, otherwise add": a(0) = 0; for n > 0, a(n) = a(n − 1) − n if that number is positive and not already in the sequence, otherwise a(n) = a(n − 1) + n, whether or not that number is already in the sequence. A005132: Look-and-say sequence
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In the string representing the integer x, the n th digit is 1 if F −n appears in the sum that represents x; that digit is 0 otherwise. For example, 24 may be represented by the string 100101001, which has the digit 1 in places 9, 6, 4, and 1, because 24 = F −1 + F −4 + F −6 + F −9 . The integer x is represented by a string of odd ...