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Mathematics & Computation III
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 The roots of any algebraic equation are complex numbers which can be depicted
as labeling points in what is called the complex plane. Proof of the fundamental
theorem of algebra was only one of the many achievements of Carl Friedrich
Gauss (1777-1855), the "Prince of Mathematics." The Gaussian distribution
and the magnetic unit gauss bear his name. (Detail) His construction of an equilateral 17-sided polygon inside a circle with
only straight edge and compass, the first such new construction since
Greek times, is the subject of this East German stamp. |
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Augustin Cauchy (1789-1857) was a prolific mathematician whose 200th birthday is commemorated on this French stamp. Besides his portrait, we see the Cauchy integral formula at right: the Cauchy integral of a regular analytic function f(z) of a complex variable is evaluated along a closed, smooth curve L in a domain D. Several paths are indicated, all enclosing the pole a. The value of these contour integrals is f(a) while contour integrals of a function not enclosing a pole are all equal to zero. On the left side of the stamp is another type of Cauchy integral, this time of a real variable, x. The function is a parabola, y=x2, and the definite integral is over the span -1=< x =<+1. It can be written as a limit as the increments along the x axis approach 0. (Detail) |
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The significant contributions of Evariste Galois (1811-1832) to the foundation of group theory were not widely recognized until many years after his untimely death in a duel in 1832. On the eve of his death he entrusted a resume of the mathematical ideas and writings that occopied his mind, including the discovery of the connection of the theory of groups with the solution of equations by radicals, to his friend Auguste Chevalier. Not until 1846 were these collected writings published by Liouville in th e Journal de Mathematiques Pures et Appliquees. (Detail) |
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Nikolai Lobachevsky (1792-1856) was a Russian mathematician who published the first non-Euclidean geometry, which does not make use of Euclid's fifth postulate, but treats Euclidian geometry as a special case. (Detail) The Lobachevskian plane, in accordance with Poincare's conformal mapping, is shown on the Finnish stamp at the head of this chapter. It is presented as interior of a circle, and lines are represented by arcs of circles orthogonal to the main circle . |
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Janos Bolyai (1802-1860) was a gifted young Hungarian mathematician who also gave thought to Euclid's geometry and came up with another system of non-Euclidean geometry while still in his twenties. He did not publish this, however, because through his father Farkas Bolyai, a friend of Gauss's, he heard that Gauss had "been there, done that", so to speak, without actually publishing. This claim by the great Prince of Mathematics was enough to discourage young Janos, but his treatise was nevertheless published later by his father in 1832. |
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Friedrich Wilhelm Bessel (1784-1846) was a German astronomer and mathematician who is remembered for the functions bearing his name; the Bessel functions of first and second order appear on this German stamp. (Detail) Bessel was the first to measure the parallax of a star (Cygni 61) in 1838, thus making it possible to calculate its distance. Observing the motions of the stars Sirius and Procyon, he deduced that each was orbiting around another, dark star. These dark stars were later found to be white dwarfs. |
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August Ferdinand Moebius (1790-1868), another astronomer and mathematician, was one of the founders of topology. His Moebius strip is a strip whose ends are joined after giving it a half twist; it has only one side and one edge, and here promotes a mathematical congress in Brazil. (Detail) |
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Charles Babbage (1792-1871) was responsible for the invention of an early antecedent of the modern computer, the analytical engine. There was much interest in calculating devices in his time, but the technology to make the analytical engine work was not yet available. (Detail) |
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 Niels Henrik Abel (1802-1829) was a Norwegian mathematician of great talent
whose work was in analysis and elliptic functions. He proved that it was
impossible to solve algebraically an equation of the fifth degree. Always
poor, he died of tuberculosis at an early age, just before the news of
an important appointment in Berlin could reach him. (Detail) |
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 Sir William Rowan Hamilton (1805-1865) was an Irish mathematician who
devised a non-commutative four-dimensional algebra of quaternions, or
hypercomplex numbers. Their importance lay in their applications in geometry
and mathematical physics, leading to vector theory. The Irish stamp at
left shows Hamilton's rules for multiplication of quaternions. (Detail) |
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