Lorenzo Mascheroni | |
|---|---|
 | |
| Born | (1750-05-13)13 May 1750 |
| Died | 14 July 1800(1800-07-14) (aged 50) |
| Occupations |
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| Known for | Mohr–Mascheroni theorem Euler–Mascheroni constant |
| Scientific career | |
| Institutions | University of Pavia |
| Ecclesiastical career | |
| Religion | Christianity |
| Church | Catholic Church |
| Ordained | 1774 |
Lorenzo Mascheroni (Italian pronunciation:[loˈrɛntsomaskeˈroːni]; 13 May 1750 – 14 July 1800) was anItaliangeometer andmathematician best known for proving that all Euclidean constructions achievable with a compass and straightedge can also be done using only a compass (Mohr–Mascheroni theorem). He also calculated theEuler–Mascheroni constant to 32 decimal places.
Lorenzo Mascheroni was born on 13 May 1750 in Castagneta, nearBergamo,Lombardy, to a wealthy merchant family. Afterseminary studies in Bergamo, he was ordained aCatholic priest in 1774, at the age of 17. His early interest in literary writing, in both Italian andLatin, was increasingly displaced by scientific – especially mathematical – studies. At first a professor ofrhetoric, from 1778 he began teachingmathematics andphysics at the seminary in Bergamo.
In 1786, Mascheroni succeededPietro Paoli as professor of mathematics at theUniversity of Pavia and in 1789, he became the rector of the university, a position he held for the next four years. In 1790 and 1792, respectively, Mascheroni published two very important memoirs in which he was able to rectify the value ofEuler's constant, reaching the calculus of thirty-two decimal digits.[1]
Though a priest, Mascheroni was sympathetic to the ideals of theFrench Revolution.[2] He enthusiastically supported the French armies that invaded Italy in 1796–99 and played a major role in the government of theCisalpine Republic.Napoleon personally knew and admired Mascheroni and was instrumental in bringing his work to the attention of the learned circles of France.[3] According toHoward Eves, thetheorem and aconstruction problem bearing Napoleon's name were discovered by Mascheroni, who let the Emperor claim them for himself.[4]
In 1797, Mascheroni was invited toParis as a member of the international commission that created themetric system.[5] During his stay in Paris, Mascheroni taught at various schools and made the acquaintance ofLagrange,Laplace, andMonge. On the occasion of the death of the mathematician andphysicistJean-Charles de Borda, he composed anelegy in Latin in his honour (1799). Mascheroni was unable to return to Italy due to the Austro-Russian invasion of Milan in 1799. He died in Paris the following year.[6] On his death, his friendVincenzo Monti dedicated to him the poemIn morte di Lorenzo Mascheroni (three cantos published in 1801).
Mascheroni was a member of theAccademia Galileiana of Padua, theRoyal Academy of Science and Letters of Mantua and theAccademia nazionale delle scienze. During his life, he published a substantial number of mathematical writings, the best known of which was hisGeometria del Compasso (Geometry of the Compass, 1797).
In his work,Geometria del Compasso (Pavia, 1797), Mascheroni proved that any geometrical construction which can be done withcompass and straightedge, can also be done with compasses alone. Mascheroni'sGeometria del Compasso had a huge impact on the scientific community. It was soon translated intoFrench by Antoine-Michel Carette (Paris, 1798), and intoGerman by Johann Philipp Gruson (Berlin, 1825). A revised and augmented edition of the French translation was published in Paris and Brussels in 1828.
However, the priority for this result (now known as theMohr–Mascheroni theorem) belongs to theDaneGeorg Mohr, who had previously published a proof in 1672 in an obscure book,Euclides Danicus. Mohr's book was overlooked by European mathematicians, and Mascheroni, like the rest of thescientific community, was unaware of it, so it is Mascheroni whose name is generally associated with this result.[7]
In hisAdnotationes ad calculum integralem Euleri (1790), Mascheroni extended several ofEuler's results, especially those involving theEuler–Mascheroni constant, usually denoted asγ (gamma). Mascheroni was able to rectify Euler's value forγ and attempted to calculate the constant to 32 decimal places, but made errors in the 20th–22nd and 31st–32nd decimal places; starting from the 20th digit, he calculated ...1811209008239 when the correct value is ...0651209008240. The figure was corrected byJohann Georg von Soldner in 1809. Mascheroni'sAdnotationes have been reprinted as an appendix in Euler'sOpera Omnia.[8]
