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  2. Indole - Wikipedia

    en.wikipedia.org/wiki/Indole

    Indole is an organic compound with the formula C 6 H 4 CCNH 3. Indole is classified as an aromatic heterocycle. It has a bicyclic structure, consisting of a six-membered benzene ring fused to a five-membered pyrrole ring. Indoles are derivatives of indole where one or more of the hydrogen atoms have been replaced by substituent groups.

  3. Urn problem - Wikipedia

    en.wikipedia.org/wiki/Urn_problem

    [4] multinomial distribution: there are balls of more than two colors. Each time a ball is extracted, it is returned before drawing another ball. [3] This is also known as 'Balls into bins'. negative binomial distribution: number of draws before a certain number of failures (incorrectly colored draws) occurs.

  4. Bertrand paradox (probability) - Wikipedia

    en.wikipedia.org/wiki/Bertrand_paradox_(probability)

    The Bertrand paradox is a problem within the classical interpretation of probability theory. Joseph Bertrand introduced it in his work Calcul des probabilités (1889) [1] as an example to show that the principle of indifference may not produce definite, well-defined results for probabilities if it is applied uncritically when the domain of possibilities is infinite.

  5. Indole test - Wikipedia

    en.wikipedia.org/wiki/Indole_test

    Indole test positive: appearance of pink layer at top (e.g. Escherichia coli) Like many biochemical tests on bacteria, results of an indole test are indicated by a change in color following a reaction with an added reagent. Pure bacterial culture must be grown in sterile tryptophan or peptone broth for 24–48 hours before performing the test.

  6. Napoleon's theorem - Wikipedia

    en.wikipedia.org/wiki/Napoleon's_theorem

    Given a hexagon A 1 A 2 A 3 A 4 A 5 A 6 with equilateral triangles constructed on the sides, either inwardly or outwardly, and the apexes of the equilateral triangles labelled B i. If G 1 , G 3 , G 5 are the respective centroids of B 6 B 1 B 2 , B 2 B 3 B 4 , B 4 B 5 B 6 , then G 1 , G 3 , G 5 form an equilateral triangle.

  7. Formulas for generating Pythagorean triples - Wikipedia

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

    Then 3 new triples [a 1, b 1, c 1], [a 2, b 2, c 2], [a 3, b 3, c 3] may be produced from [a, b, c] using matrix multiplication and Berggren's [11] three matrices A, B, C. Triple [a, b, c] is termed the parent of the three new triples (the children). Each child is itself the parent of 3 more children, and so on.

  8. para-Dimethylaminobenzaldehyde - Wikipedia

    en.wikipedia.org/wiki/Para-Dimethylaminobenzaldehyde

    para-Dimethylaminobenzaldehyde is an organic compound containing amine and aldehyde moieties which is used in Ehrlich's reagent and Kovac's reagent to test for indoles.The carbonyl group typically reacts with the electron rich 2-position of the indole but may also react at the C-3 or N-1 positions. [2]

  9. Fischer indole synthesis - Wikipedia

    en.wikipedia.org/wiki/Fischer_indole_synthesis

    The Fischer indole synthesis is a chemical reaction that produces the aromatic heterocycle indole from a (substituted) phenylhydrazine and an aldehyde or ketone under acidic conditions. [1] [2] The reaction was discovered in 1883 by Emil Fischer. Today antimigraine drugs of the triptan class are often synthesized by this method. The Fischer ...