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A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
Lucas numbers have L 1 = 1, L 2 = 3, and L n = L n−1 + L n−2. Primefree sequences use the Fibonacci recursion with other starting points to generate sequences in which all numbers are composite. Letting a number be a linear function (other than the sum) of the 2 preceding numbers. The Pell numbers have P n = 2P n−1 + P n−2.
In computer science, a lookup table (LUT) is an array that replaces runtime computation with a simpler array indexing operation, in a process termed as direct addressing.The savings in processing time can be significant, because retrieving a value from memory is often faster than carrying out an "expensive" computation or input/output operation. [1]
Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS.It features calculation or computation capabilities, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications (VBA).
The only known powers of 2 with all digits even are 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^6 = 64 and 2^11 = 2048. [11] The first 3 powers of 2 with all but last digit odd is 2^4 = 16, 2^5 = 32 and 2^9 = 512. The next such power of 2 of form 2^n should have n of at least 6 digits.
In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations).For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange.
The following are important identities in vector algebra.Identities that only involve the magnitude of a vector ‖ ‖ and the dot product (scalar product) of two vectors A·B, apply to vectors in any dimension, while identities that use the cross product (vector product) A×B only apply in three dimensions, since the cross product is only defined there.
Leonardo of Pisa (c. 1170 – c. 1250) described this method [1] [2] for generating primitive triples using the sequence of consecutive odd integers ,,,,, … and the fact that the sum of the first n terms of this sequence is .