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  2. Formulas for generating Pythagorean triples - Wikipedia

    en.wikipedia.org/wiki/Formulas_for_generating...

    Michael Stifel published the following method in 1544. [3] [4] Consider the sequence of mixed numbers,,,, … with = + +.To calculate a Pythagorean triple, take any term of this sequence and convert it to an improper fraction (for mixed number , the corresponding improper fraction is ).

  3. Guess 2/3 of the average - Wikipedia

    en.wikipedia.org/wiki/Guess_2/3_of_the_average

    Guess 2/3 of the average. In game theory, " guess ⁠ 2 3 ⁠ of the average " is a game that explores how a player’s strategic reasoning process takes into account the mental process of others in the game. [ 1] In this game, players simultaneously select a real number between 0 and 100, inclusive. The winner of the game is the player (s) who ...

  4. Fibonacci sequence - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_sequence

    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.

  5. Pythagorean triple - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_triple

    A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A triangle whose side lengths are a Pythagorean triple is a right triangle and ...

  6. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or ⁠ ⁠, where a and b are both integers. [ 9] As with other fractions, the denominator ( b) cannot be zero. Examples include ⁠ 1 2 ⁠, − ⁠ 8 5 ⁠, ⁠ −8 5 ⁠, and ⁠ 8 −5 ⁠.

  7. Derivative - Wikipedia

    en.wikipedia.org/wiki/Derivative

    In mathematics, the derivative is a fundamental tool that quantifies the sensitivity of change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.

  8. Repeating decimal - Wikipedia

    en.wikipedia.org/wiki/Repeating_decimal

    Repeating decimal. A repeating decimal or recurring decimal is a decimal representation of a number whose digits are eventually periodic (that is, after some place, the same sequence of digits is repeated forever); if this sequence consists only of zeros (that is if there is only a finite number of nonzero digits), the decimal is said to be ...

  9. Cholecalciferol - Wikipedia

    en.wikipedia.org/wiki/Cholecalciferol

    Cholecalciferol is a form of vitamin D which is naturally synthesized in skin and functions as a pro-hormone, being converted to calcitriol. This is important for maintaining calcium levels and promoting bone health and development. [ 4] As a medication, cholecalciferol may be taken as a dietary supplement to prevent or to treat vitamin D ...

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