**Karl Mollweide** was a German mathematician and astronomer. He invented a map projection called the Mollweide projection.

- Unlike most people who become leading mathematicians, Mollweide showed no interest in or talent for the subject while in elementary school.
- With a love of mathematics and a considerable talent for the subject, it was natural that Mollweide would want to study the subject to a higher level.
- Pfaff had much in common with Mollweide for both had studied mathematics largely on their own.
- Mollweide entered the University of Helmstedt in 1793 and spent three years studying there.
- Pfaff was an excellent teacher and at that time was working hard to build up a flourishing mathematics department so Mollweide was happy to be offered a teaching position at the university following his undergraduate studies.
- This was not the only problem faced by the new lecturer Mollweide for he was suffering severe health problems (probably caused by depression) which forced him to give up his position at Helmstedt after about a year and return to his home.
- Back home Mollweide took it easy and spent the next two years essentially taking a prolonged rest.
- The first of these was his invention of the Mollweide projection of the sphere, a map projection which he produced to correct the distortions in the Mercator projection, first used by Gerardus Mercator in 1569.
- Mollweide announced his projection in 1805.
- To correct these defects, Mollweide drew his elliptical projection; but in preserving the correct relation between the areas he was compelled to sacrifice configuration and angular measurement.
- Aesthetically, Mollweide's map, which represents the whole world in an ellipse whose axes are in a 2:1 ratio, reflects the essentially round character of the earth better than rectangular maps.
- The Mollweide projection is distortion-free along the parallels 40.7 degrees North and South.
- The second piece of work to which Mollweide's name is attached today is the Mollweide equations which are sometimes called Mollweide's formulas.
- These trigonometric identities appear in Mollweide's paper Zusätze zur ebenen und sphärischen Trigonometrie Ⓣ(Additions to plane and spherical trigonometry) (1808).
- One of the more puzzling aspects is why these equations should have become known as the Mollweide equations since in the 1808 paper in which they appear Mollweide refers the book by Antonio Cagnoli (1743-1816) Traité de Trigonométrie Rectiligne et Sphérique, Contenant des Méthodes et des Formules Nouvelles, avec des Applications à la Plupart des Problêmes de l'astronomie Ⓣ(containing methods and new formulas with applications to most astronomical problems) (1786) which contains the formulas.
- However, the formulas go back to Isaac Newton, or even earlier, but there is no doubt that Mollweide's discovery was made independently of this earlier work.
- In 1811 Mollweide left Halle when he was named Professor of Astronomy at the University of Leipzig.
- At this time Möbius was intending to make a career as an astronomer but after being taught by Mollweide he became, like his teacher, equally interested in both mathematics and astronomy.
- As well as being Professor of Astronomy at Leipzig, Mollweide was also director of the university observatory.
- All this concentration on war had made Mollweide's life extremely difficult for he was forced to concentrate on geographic studies to assist the war effort.
- Mollweide, always more enthusiastic towards mathematics than astronomy, decided in 1814 to move from being Professor of Astronomy to Professor of Mathematics, still at the University of Leipzig.
- From 1820 to 1823 Mollweide was Dean of the Leipzig University Faculty of Philosophy.
- We referred above to the two contributions for which Mollweide is best remembered today.
- Mollweide was admired as a lecturer because of his ability to present dry topics in an interesting manner by drawing connections to other topics.
- Among his mathematical contributions, Mollweide was the first to use the modern congruence symbol in the 1824 edition of Lorenz's German translation of 'Euklid's Elemente'.

Born 3 February 1774, Wolfenbüttel, Brunswick, now Germany. Died 10 March 1825, Leipzig, Germany.

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Astronomy, Origin Germany

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