Jacques Bernoulli
Definition
Proper noun A Swiss mathematician (1654-1705), also known as Jacob Bernoulli, who made significant contributions to calculus and probability theory. He is particularly known for his work on the mathematical constant e, the Bernoulli numbers, and the law of large numbers in probability.
Usage
The term "Jacques Bernoulli" is used to refer to the historical figure, his discoveries, and mathematical concepts named after him. * Jacques Bernoulli was a prominent member of the famous Bernoulli family of mathematicians. * The Bernoulli differential equation is named after Jacques Bernoulli. * In many historical texts, Jacques Bernoulli is also referred to by his German name, Jacob Bernoulli.
Advanced Usage
- Eponymous Usage: Many mathematical concepts bear his name, often using the anglicized form "Bernoulli." For example: Bernoulli's inequality, Bernoulli polynomials, and Bernoulli trials in probability.
- Historical Context: When discussing the history of calculus and its development alongside Leibniz and Newton, is frequently cited as an important contributor.
Variants and Related Words
- Jacob Bernoulli: The more common German/Latin form of his name, frequently used interchangeably in academic literature.
- Bernoulli: The family name, often used to refer to the collective work of the Bernoulli family (including his brother Johann and nephew Daniel).
- Bernoulli Number (n): A sequence of rational numbers with deep connections to number theory, discovered by Jacques Bernoulli.
- Bernoulli's Law of Large Numbers (n): A fundamental theorem in probability theory stating that the average of a large number of independent trials converges to the expected value.
Synonyms
- Jacob Bernoulli
- James Bernoulli (an older English translation)
Related Phrases and Concepts
- Bernoulli Trial: A random experiment with exactly two possible outcomes, "success" and "failure."
- Bernoulli Distribution: The probability distribution of a random variable which takes the value 1 with probability and the value 0 with probability .
- Ars Conjectandi: The title of his posthumously published seminal work on probability theory, often translated as "The Art of Conjecturing."
Noun
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Swiss mathematician (1654-1705)
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