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  2. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    For instance, the first counterexample must be odd because f(2n) = n, smaller than 2n; and it must be 3 mod 4 because f 2 (4n + 1) = 3n + 1, smaller than 4n + 1. For each starting value a which is not a counterexample to the Collatz conjecture, there is a k for which such an inequality holds, so checking the Collatz conjecture for one starting ...

  3. Division (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Division_(mathematics)

    In terms of partition, 20 / 5 means the size of each of 5 parts into which a set of size 20 is divided. For example, 20 apples divide into five groups of four apples, meaning that "twenty divided by five is equal to four". This is denoted as 20 / 5 = 4, or ⁠ 20 / 5 ⁠ = 4. [2] In the example, 20 is the dividend, 5 is the divisor, and 4 is ...

  4. Division algorithm - Wikipedia

    en.wikipedia.org/wiki/Division_algorithm

    A division algorithm is an algorithm which, given two integers N and D (respectively the numerator and the denominator), computes their quotient and/or remainder, the result of Euclidean division. Some are applied by hand, while others are employed by digital circuit designs and software. Division algorithms fall into two main categories: slow ...

  5. Inverse-square law - Wikipedia

    en.wikipedia.org/wiki/Inverse-square_law

    He illustrates that F and Φ obey the formulas F ∝ 1 / R^2 sinh^2(r/R) and Φ ∝ coth(r/R), where R and r represent the curvature radius and the distance from the focal point, respectively. [11] The concept of the dimensionality of space, first proposed by Immanuel Kant, is an ongoing topic of debate in relation to the inverse-square law. [12]

  6. Mental calculation - Wikipedia

    en.wikipedia.org/wiki/Mental_calculation

    0 3 = 0; 1 3 = 1 up 1; 2 3 = 8 down 3; 3 3 = 27 down 1; 4 3 = 64 down 3; 5 3 = 125 up 1; 6 3 = 216 up 1; 7 3 = 343 down 3; 8 3 = 512 down 1; 9 3 = 729 down 3; 10 3 = 1000 up 1; There are two steps to extracting the cube root from the cube of a two-digit number. For example, extracting the cube root of 29791. Determine the one's place (units) of ...

  7. Greatest common divisor - Wikipedia

    en.wikipedia.org/wiki/Greatest_common_divisor

    Greatest common divisor. In mathematics, the greatest common divisor ( GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted . For example, the GCD of 8 and 12 is 4, that is, gcd (8, 12) = 4. [ 1][ 2]

  8. Elastography - Wikipedia

    en.wikipedia.org/wiki/Elastography

    One strength of MRE is the resulting 3-D elasticity map, which can cover an entire organ. [2] Because MRI is not limited by air or bone, it can access some tissues ultrasound cannot, notably the brain. It also has the advantage of being more uniform across operators and less dependent on operator skill than most methods of ultrasound elastography.

  9. Multiplicative inverse - Wikipedia

    en.wikipedia.org/wiki/Multiplicative_inverse

    The graph forms a rectangular hyperbola. In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/ x or x1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a / b is b / a. For the multiplicative inverse of a real number, divide 1 by the number.