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Monday, October 19, 2009

THE INTEGRAL SYMBOL







  • The ∫ symbol is used to denote integral in mathematics.

  •  The notation was introduced by the German mathematician Gottfried Wilhelm von Leibniz towards the end of the 17th century.  

  • The symbol chosen to be a stylized script "S" (long s ) because the integral is a limit of sums.

Euler's depiction on SWISS 10 FRANC NOTE


EULER'S POWERS OF MEMORY AND CONCENTRATION

Euler's powers of memory and concentration were legendary :


Euler's eyesight worsened throughout his mathematical career. Three years after suffering a near-fatal fever in 1735 he became nearly blind in his right eye, but Euler rather blamed his condition on the painstaking work on cartography he performed for the St. Petersburg Academy.

Euler's sight in that eye worsened throughout his stay in Germany, so much so that Frederick referred to him as " Cyclops".

Euler later suffered a cataract in his good left eye, rendering him almost totally blind a few weeks after its discovery in 1766.

Even so, his condition appeared to have little effect on his productivity, as he compensated for it with his mental calculation skills and photographic memory.

For example: Euler could repeat the Aeneid of virgil from beginning to end without hesitation, and for every page in the edition he could indicate which line was the first and which the last.

With the aid of his scribes, Euler's productivity on many areas of study actually increased. He produced on average one mathematical paper every week in the year 1775.

JOHANN CARL FRIEDRICH GAUSS

 PRINCE OF MATHEMATICS

Johann Carl Friedrich Gauss , a German mathematician who had a remarkable influence in many fields , including number theory, statistics, analysis, differential geometry, electrostatics, astronomy and optics is ranked as one of history's most influential mathematicians.
CHILD PRODIGY:


At the age of three he amazed his father by correcting an arithmetical error.

In primary school his teacher, J.G. B├╝ttner, tried to occupy pupils by making them add a list of integers. The young Gauss reputedly produced the correct answer within seconds, to the astonishment of his teacher. 

Gauss's presumed method, which supposes the list of numbers was from 1 to 100, was to realize that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums:


1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on, for a total sum of 50 × 101 = 5050 .


FAMOUS QUOTE:
“Mathematics is the queen of the sciences and number theory is the queen of mathematics”
“Ask her to wait a moment,I am almost done” (he told this while working when he was informed that his wife is dying).
CONTRIBUTIONS:

  • In Disquisitiones Arithmeticae, one of the most brilliant achievements in mathematics, Gauss systematized the study of number theory. This work was fundamental in consolidating number theory as a discipline and has shaped the field to the present day.
  • Gauss proved the Fundamental Theorem of Algebra, which states that every polynomial has a root of the form a+bi.
  • He also discovered the Cauchy Integral theorem for analytic functions
  • Gauss's work in mathematical physics contributed to potential theory and the development of the Principle of Conservation of Energy.
  • Theoria motus corporum celestium (theory of motion of the celestial bodies) is his most significant work on applied mathematics.
  • Gauss discovered Ceres, the largest of the asteroids orbiting around the Sun.
  • His Theory of Celestial Movement remains a cornerstone of astronomical computation. It introduced the Gaussian gravitational constant.
  • Introduced the Method of Least Squares, a procedure used in all sciences to this day to minimize the impact of measurement error.


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