# The Penguin Dictionary of Curious and Interesting Numbers

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It will be observed, that I had not the usual stimulus for desiring personal reputation, the desire, namely, to float amidst the conversation of men. And this is done by referring to deep relations between deep mathematical concepts that often link different mathematical domains (Manders 1989). The discussion of conic sections by the ancient Greeks, see the wikipedia article, gave the basic definitions required by Kepler to formulate his law of planetary orbits. The theories of strings and crystals have benefited from Ramanujan's work. (Today some professors achieve fame just by finding a new proof for one of Ramanujan's many results.) Unlike Abel, who insisted on rigorous proofs, Ramanujan often omitted proofs. (Ramanujan may have had unrecorded proofs, poverty leading him to use chalk and erasable slate rather than paper.) Unlike Abel, much of whose work depended on the complex numbers, most of Ramanujan's work focused on real numbers.

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That argument is called the principal argument, arg z, where: ÷ t < principal argument s t. Small class sizes, lots of hands-on, lots of writing, and lots of time spent teaching to learn rather than teaching to a standardized test. Pomerance, in Number Theory, CNTA Proceedings, Montreal, 2002, CRM Proc. It cost Edward some exertion of activity to attain the place which Fergus's followers occupied in the line of march.

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Different geometries allow strings to vibrate in different ways, just as tightening the tension on a drum changes its pitch. For I doubt not, but if it had been a thing contrary to any mans right of dominion, or to the interest of men that have dominion, That the three Angles of a Triangle, should be equall to two Angles of a Square; that doctrine should have been, if not disputed, yet by the burning of all books of Geometry, suppressed, as far as he whom it concerned was able.

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Yet even there his imagination, the predominant faculty of his mind, was frequently excited. Introduction • Ant Odometer (c. 150 million BC) • Primates Count (c. 30 million BC) • Cicada-Generated Prime Numbers (c. 1 million BC) • Knots (c. 100,000 BC) • Ishango Bone (c. 18,000 BC) • Quipu (c. 3000 BC) • Dice (c. 3000 BC) • Magic Squares (c. 2200 BC) • Plimpton 322 (c. 1800 BC) • Rhind Papyrus (c. 1650 BC) • Tic Tac Toe (c. 1300 BC) • Pythagorean Theorem and Triangles (c. 600 BC) • Go (548 BC) • Pythagoras Founds Mathematical Brotherhood (530 BC) • Zeno's Paradoxes (c. 445 BC) • Quadrature of the Lune (c. 440 BC) • Platonic Solids (350 BC) • Aristotle's Organon (c. 350 BC) • Aristotle's Wheel Paradox (c. 320 BC) • Euclid's Elements (300 BC) • Archimedes: Sand, Cattle & Stomachion (c. 250 BC) • pi (c. 250 BC) • Sieve of Eratosthenes (c. 240 BC) • Archimedean Semi-Regular Polyhedra (c. 240 BC) • Archimedes' Spiral (225 BC) • Cissoid of Diocles (c. 180 BC) • Ptolemy's Almagest (c. 150) • Diophantus's Arithmetica (250) • Pappus's Hexagon Theorem (c. 340) • Bakhshali Manuscript (c. 350) • The Death of Hypatia (415) • Zero (c. 650) • Alcuin's Propositiones ad Acuendos Juvenes (c. 800) • al-Khwarizmi's Algebra (830) • Borromean Rings (834) • Ganita Sara Samgraha (850) • Thabit Formula for Amicable Numbers (c. 850) • Kitab al-fusul fi al-hisab al-Hindi (c. 953) • Omar Khayyam's Treatise (1070) • Al-Samawal's The Dazzling (c. 1150) • Abacus (c. 1200) • Fibonacci's Liber Abaci (1202) • Wheat on a Chessboard (1256) • Harmonic Series Diverges (c. 1350) • Law of Cosines (c. 1427) • Treviso Arithmetic (1478) • Discovery of Series Formula for Pi (c. 1500) • Golden Ratio (1509) • Polygraphiae Libri Sex (1518) • Loxodrome (1537) • Cardano's Ars Magna (1545) • Sumario Compendioso (1556) • Mercator Projection (1569) • Imaginary Numbers (1572) • Kepler Conjecture (1611) • Logarithms (1614) • Slide Rule (1621) • Fermat's Spiral (1636) • Fermat's Last Theorem (1637) • Descartes' La Geometrie (1637) • Cardioid (1637) • Logarithmic Spiral (1638) • Projective Geometry (1639) • Torricelli's Trumpet (1641) • Pascal's Triangle (1654) • The Length of Neile's Semicubical Parabola (1657) • Viviani's Theorem (1659) • Discovery of Calculus (c. 1665) • Newton's Method (1669) • Tautochrone Problem (1673) • Astroid (1674) • L'Hopital's Analysis of the Infinitely Small (1696) • Rope around the Earth Puzzle (1702) • Law of Large Numbers (1713) • Euler's Number, e (1727) • Stirling's Formula (1730) • Normal Distribution Curve (1733) • Euler-Mascheroni Constant (1735) • Konigsberg Bridges (1736) • St.

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Vous parlez si bien l'Anglois, cela ne vous donneroit pas beaucoup do peine.'' ``Ah! pas du tout, Monseigneur,'' replied Mons. le Comte de Beaujeu, his head bending down to the neck of his little prancing highly-managed charger. The Bailie's doing what he can to save something out of the wreck for puir Rose; but I doubt, I doubt, I shall never see her again, for I maun lay my banes in some far country.'' ``Hout na, your Honour,' said old Janet; ``ye were just as ill aft in the feifteen, and got the bonnie baronie back, an a.--- And now the eggs is ready, and the muir-cock's brandered, and there's ilk ane a trencher and some saut, and the heel o' the white loaf that cam frae the Bailie's; and there's plenty o' brandy in the greybeard that Luckie Maclearie sent doun; and winna ye be suppered like princes?'' ``I wish one Prince, at least, of our acquaintance, may be no worse off,'' said the Baron to Waverley, who joined him in cordial hopes for the safety of the unfortunate Chevalier.

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Perhaps the most interesting of these areas is topology. He looked dubiously at Waverley as he approached the little green rail which fenced his desk and stool from the approach of the vulgar. With her, and sister Theresa, the priest proposed next day to leave Carlisle, for the nearest seaport from which they could embark for France. Morton, where they can sue out their Habeas Corpus.'' ``But I cannot see that this youth's guilt is at all established to my satisfaction,'' said the clergyman. ``Because your good nature blinds your good sense,'' replied Major Melville. ``Observe now: this young man, descended of a family of hereditary Jacobites, his uncle the leader of the Tory interest in the county of ------, his father a disobliged and discontented courtier, his tutor a non-juror, and the author of two treasonable volumes---this youth, I say, enters into Gardiner's dragoons, bringing with him a body of young fellows from his uncle's estate, who have not stickled at avowing, in their way, the high church principles they learned at Waverley-Honour, in their disputes with their comrades.

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This garb, which resembled the dress often put on children in Scotland, called a polorde (i.e. polonaise), is a very ancient modification of the Highland garb. From this aperture he beheld the wretched Gaston suspended by the neck, by his own girdle, to an iron ring in the side of his prison. I have already hinted, that the dainty, squeamish, and fastidious taste acquired by a surfeit of idle reading, had not only rendered our hero unfit for serious and sober study, but had even disgusted him in some degree with that in which he had hitherto indulged.

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Matches were then made for running, wrestling, leaping, pitching the bar, and other sports, in which this feudal militia displayed incredible swiftness, strength, and agility; and accomplished the purpose which their Chieftain had at heart, by impressing on Waverley no light sense of their merit as soldiers, and of the power of him who commanded them by his nod.< *> of uncommon acuteness, fire, and ambition, which, as he became acquainted with the state of the country, gradually assumed a mixed and peculiar tone, that could only have been acquired Sixty Years since. ``And what number of such gallant fellows have the happiness to call you leader?'' asked Waverley. ``In a good cause, and under a chieftain whom they loved, the race of Ivor have seldom taken the field under five hundred claymores.

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For a more abstract example, consider three colored blocks (red, green, and blue), initially placed in the order RGB. After this, put your faith in princes!'' ``End? And now, since my time is short, let me come to the questions that interest me most---The Prince? has he escaped the blood-hounds?'' ``Praised be God for that! Mathematically, it can be shown that with an infinite number of toothpick drops, the probability actually equals pi.

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An outcome of all this foundational activity was a thorough reworking of geometry, this time as a collection of formal theories within the predicate calculus. Bradwardine, as confirming or illustrating his own favourite anecdotes. He had observed with great satisfaction the growing attachment of Waverley to his sister, nor did he see any bar to their union, excepting the situation which Waverley's father held in the ministry, and Edward's own commission in the army of George II.