Jurij Vega

Baron Jurij Bartolomej Vega (also correct Veha; official Latin Georgius Bartholomaei Vecha; German Georg Freiherr von Vega) (March 23, 1754 – September 26, 1802) was a Slovenian mathematician, physicist and artillery officer.

Mathematical accomplishments

Vega published a series of books of logarithm tables. The first one appeared in 1783. Much later, in 1797 it was followed by a second volume that contained a collection of integrals and other useful formulae. His Handbook, which was originally published in 1793, was later translated into several languages and appeared in over 100 issues. His major work was Zakladnica vseh logaritmov (Thesaurus Logarithmorum Completus or Treasury of all Logarithms) that was first published 1794 in Leipzig. An engineer, Franc Allmer, honourable senator of the Technical university of Graz, has found Vega's logarithmic tables with 10 decimal places in the Museum of Carl Friedrich Gauss in Göttingen. Gauss used this work frequently and he has written in it several calculations. Gauss has also found some of Vega's errors in the calculations in the range of numbers, of which there are more than a million. A copy of Vega's Thesaurus belonging to the private collection of the British mathematician and computing pioneer Charles Babbage (1791-1871) is preserved at the Royal Observatory at Edinburgh.

Related Topics:
Logarithm - 1783 - 1797 - Thesaurus Logarithmorum Completus - 1794 - Leipzig - Graz - Decimal - Göttingen - Gauss - Charles Babbage - Royal Observatory at Edinburgh

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Over the years Vega wrote a four volume textbook Vorlesungen über die Mathematik (Lectures about Mathematics). Volume I appeared in 1782 when he was 28 years old, Volume II in 1784, Volume III in 1788 and Volume IV in 1800. His textbooks also contain interesting tables: for instance, in Volume II one can find closed form expressions for sines of multiples of 3 degrees, written in a form easy to work with.

Related Topics:
1782 - 1784

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Vega wrote at least six scientific papers. On August 20, 1789 Vega achieved a world record when he calculated pi to 140 places, of which 137 were correct. This calculation he proposed to the Russian Academy of Sciences in Saint Petersburg (????? ?????????) in the booklet V. razprava (The fifth discussion), where he had found with his calculating method an error on the 113th place from the estimation of Thomas Fantet de Lagny (1660–1734) from 1719 of 127 places. Vega retained his record 52 years until 1841 and his method is mentioned still today. His article was not published by the Academy until six years later, in 1795. Vega had improved John Machin's formula from 1706:

Related Topics:
August 20 - 1789 - Pi - Russian Academy of Sciences - Saint Petersburg - 1660 - 1734 - 1719 - 1841 - John Machin - 1706

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: {piover 4} = 4 rctan left({1over 5} ight) - rctan left({1over 239} ight)

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with his formula, which is equal to Euler's formula from 1755:

Related Topics:
Euler's - 1755

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: {piover 4} = 5 rctan left({1over 7} ight) + 2 rctan left({3over 79} ight) ; ,

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and which converges faster than Machin's formula. He had checked his result with the similar Hutton's formula:

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: {piover 4} = 2 rctan left({1over 3} ight) + rctan left({1over 7} ight) ; .

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He had developed the second term in the series only once. Japanese mathematicians of that time had used two approximations :

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: ? = 3; {22/7}; {333/106}; {355/113}; {103993/33102}; {104348/33215}; {208341/66317}; {312689/99532}; {833719/265381}; {1146408/364913};

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: = = {5419351/1725033}

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: = 3.14159265358981538324194377730744861

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and

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: ? = 3; {22/7}; {333/106}; {355/113}; {1043/ 332}; {304911/97057}; {305954/97389}; {610865/194446}; {916819/291835}; {4278141/1361786}; {5194960/1653621}; {14668061/4669028}; {19863021/6322649}; {34531082/10991677}; {503298169/160206127}; {15133476152/4817175487}; {30770250473/9794557101}; {599768235139/190913760406}; {630538485612/200708317507}; {1230306720751/391622077913}; {14163912413873/4508551174550}; {15394219134624/4900173252463}; {60346569817745/19209070931939}; {75740788952369/24109244184402}; {136087358770114/43318315116341}; {211828147722483/67427559300743}; {347915506492597/110745874417084};

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: = = {1255574667200274/399665182551995}

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: = 3.14156629602561954577603945201650090

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which were found in the same manner as John Wallis' method from 1655 with the development in the infinite continued fraction: the first approximation is the sixth even approximation of the infinite continued fraction for ? and the second varies from the first in the ninth term. Both approximations differ in the 13th place. Among these Japanese mathematicians were presumably Shinsuke Seki Kowa, named also Takakazu (1640–1708) who in 1700 had found 10 places, Takebe Hikojiro Katahiro Kenko (1664–1739) who in 1722 had found 42 (41 correct) places of ?, Kamata Yoshikiyo (1678–1744) who in 1730 found 25 places and Matsunaga Yoshisuke Ryohitsu, (circa 1639–1744) who in 1739 had found 51 places of ? with the same method as Isaac Newton in 1665 with a series arcsin (1/2) = ?/6:

Related Topics:
John Wallis - 1655 - Continued fraction - 1640 - 1708 - 1700 - 1664 - 1739 - 1722 - 1678 - 1744 - 1730 - 1639 - Isaac Newton - 1665

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:  ? = 3 ( 1+{12 / (4 · 6)}+{12 · 32 / (4 · 6 · 8 · 10)} + {12 · 32 · 52 / ( 4 · 6 · 8 · 10 · 12 · 14)} + {12 · 32 · 52 · 72 / (4 · 6 · 8 · 10 · 12 · 14 · 16 · 18) } + ...),

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where for such precision one has to take about 140 terms. First approximations of infinite continued fractions of this series are:

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: ?1 = ;

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: ?2 = ;

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: ?3 = ;

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: ?4 = ;

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: ?5 = ;

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: ?6 = ;

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: ?7 = ;

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: ?8 = ;

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His method of calculating ? is still mentioned today. Although he worked in the subjects of ballistics, physics and astronomy, his major contributions are to the mathematics of the second half of the 18th century.

Related Topics:
Astronomy - 18th century

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In 1781 Vega tried to push further his idea in the Austrian Habsburg monarchy about the usage of the decimal metric system of units. His idea was not accepted, but it was introduced later under the emperor Franz Josef I in 1871.

Related Topics:
1781 - Habsburg monarchy - Metric system - Franz Josef I - 1871

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Jurij Vega was a member of the Academy of Practical Sciences in Mainz, the Physical and Mathematical Society of Erfurt, the Bohemian Scientific Society in Prague, and the Prussian Academy of Sciences in Berlin. He was also an associate member of the British Scientific Society in Göttingen. He was awarded the Order of Maria Theresa on May 11, 1796. In 1800 Jurij Vega obtained a title of hereditary baron including the right to his own coat of arms.

Related Topics:
Erfurt - Prague - Berlin - Göttingen - Maria Theresa - May 11 - 1796 - 1800

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The Slovenian PTT has issued a stamp honouring Jurij Vega and the National Bank of Slovenia has issued a 50 Tolar banknote in his honour.

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