**Georg Klügel** was a German mathematician who wrote a Dictionary of Mathematics.

- Klügel, who was his parents' first son, attended the Johanneum Grammar School, the renowned humanistic school in Hamburg.
- He was strongly encouraged by the mathematics teacher at the Hamburg Gymnasium, Johann Georg Büsch (1728-1800), and, under his guidance, made a deeper study of mathematics and physics than the curriculum required.
- Büsch, who had studied at Hamburg and Göttingen, had been appointed to the Hamburg Gymnasium as a professor in 1856 and taught Klügel for his first four years in the post.
- Despite his love and talent for the subject at the Gymnasium, Klügel did not decide to follow a mathematical career at this stage, however, and he entered Göttingen University in 1760 with the intention of reading for a degree in theology.
- At Göttingen University Klügel took a mathematics course as part of his theology degree and so he met Abraham Kästner who quickly saw his talents in mathematics.
- Klügel was fascinated by the topic and was soon ready to follow Kästner's advice and change his course to read for a degree in mathematics.
- This was particularly important since, up to the time Klügel studied it, the work had been totally neglected.
- Other attempts which Klügel examined in his thesis were by Proclus, Nicolas de Malézieu (1650-1727), Nasir al-Din al-Tusi, Johann Andreas von Segner, Johann Gustav Karsten, Samuel König, Abraham Kästner, Giordano Vitale (1633-1711), Friedrich Gottlob Hanke (1751), Christopher Clavius, Andrea Tacquet, Pietro Cataldi, Peter Ramus (with additions from the editor Lazarus Schoner) and Christian Wolff (1679-1754).
- Klügel remained in Göttingen until 1765 when he moved to Hanover to take up the appointment as editor of the Intelligenzblatt.
- The university, however, was closed in 1810, twenty years after Klügel left it, when it was incorporated into Göttingen University.
- It was at Easter 1788 that Klügel moved to the chair of mathematics and physics at the University of Halle.
- It was while he worked at the Universities of Helmstedt and Halle that Klügel made his most important contributions to mathematics.
- For example, Klügel made an exceptional contribution to trigonometry, unifying formulae and introducing the concept of trigonometric function, in his Analytische Trigonometrie Ⓣ(Analytical trigonometry) (1770).
- Leonhard Euler, who studied similar problems nine years later, in some respects achieved less than Klügel in this area.
- Klügel's trigonometry was very modern for its time and was exceptional among the contemporary textbooks.
- In the following year, the first part of his translation of Joseph Priestley's 'The History and Present State of Discoveries Relating to Vision, Light and Colours' was published, with additions by Klügel, as Geschichte und gegenwärtiger Zustand der Optik mach der Englischen Priestleys bearbeitet Ⓣ(History and present condition of the optics as the English Priestley showed).
- The second part of the translation, again with additions by Klügel, was published in 1776.
- In 1795 Klügel published Über die Lehre von den entgegengesetzten Grössen Ⓣ(On the theory of opposite sizes) which is remarkable for recognising how different motivations to develop mathematics could lead to different discoveries.
- Klügel believed that the ancient Greeks had not followed the path of seeking to generalise and had, as a consequence, not discovered negative numbers.
- In fact, although Klügel is clearly not thinking in terms of giving a historical account of these topics, he does show some interest in the history and gives certain useful pointers.
- Another three volumes were added between 1823 and 1836 by Karl Brandan Mollweide and Johann August Grunert and the dictionary was widely used for several generations making Klügel's name widely known.
- We should note that in the above biography we have mentioned a number of Klügel's major works but he also published around 70 minor works in 14 scholarly journals.
- Among the honours which Klügel received for his contributions to mathematics was election to the Berlin Academy which took place on 27 January 1803.

Born 19 August 1739, Hamburg, Germany. Died 4 August 1812, Halle, Germany.

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Origin Germany

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive