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In the letters, Pascal's tone combines the fervor of a convert with the wit and polish of a man of the world. Their style meant that, quite apart from their religious influence, the Provincial Letters were popular as a literary work. Adding to that popularity was Pascal's use of humor, mockery, and satire in his arguments.
The problem of points, also called the problem of division of the stakes, is a classical problem in probability theory.One of the famous problems that motivated the beginnings of modern probability theory in the 17th century, it led Blaise Pascal to the first explicit reasoning about what today is known as an expected value.
Pascal's triangle, rows 0 through 7. The hockey stick identity confirms, for example: for n =6, r =2: 1+3+6+10+15=35. In combinatorics , the hockey-stick identity , [ 1 ] Christmas stocking identity , [ 2 ] boomerang identity , Fermat's identity or Chu's Theorem , [ 3 ] states that if n ≥ r ≥ 0 {\displaystyle n\geq r\geq 0} are integers, then
Blaise Pascal's works: text, concordances and frequency lists "Blaise Pascal" . Catholic Encyclopedia. 1913. Etext of Pascal's Pensées (English, in various formats) Etext of Pascal's Lettres Provinciales (English) Etext of a number of Pascal's minor works (English translation) including, De l'Esprit géométrique and De l'Art de persuader.
The 16-year-old Blaise Pascal demonstrates the properties of the hexagrammum mysticum in his Essai pour les coniques which he sends to Mersenne.; October 18 – Fermat states his "little theorem" in a letter to Frénicle de Bessy: if p is a prime number, then for any integer a, a p − a will be divisible by p.
Fermat sent the letters in which he mentioned the case in which n = 3 in 1636, 1640 and 1657. [31] Euler sent a letter to Goldbach on 4 August 1753 in which claimed to have a proof of the case in which n = 3. [32] Euler had a complete and pure elementary proof in 1760, but the result was not published. [33] Later, Euler's proof for n = 3 was ...
Bernard Frénicle de Bessy (c. 1604 – 1674), was a French mathematician born in Paris, who wrote numerous mathematical papers, mainly in number theory and combinatorics.He is best remembered for Des quarrez ou tables magiques, a treatise on magic squares published posthumously in 1693, in which he described all 880 essentially different normal magic squares of order 4.
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation a n + b n = c n for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions. [1]