Firstly,wehaveprovidedahistoricaloutlineofthegeometricalcalculusandgeometricalalgebra duringthesecondpartofXIXcenturyandthefirstyearsofXXcentury.Subsequently,ouraimhasbeentohighlight through this period in Italy, and in the international context (comparison with Euge Áne Prouhet (1817-1867), CharlesSturm(1803-1855),GustavRobertKirchhoff(1824-1887),OsipIvanovichSomoff(1815-1876),PaulAppell (1855-1930),OttoFo Èppl(1854-1924)andothers)thedidacticuseofgeometricalcalculus(andofthehomographies) intheuniversitytreatisesofmechanicsandofmathematicalphysics.Inthishistoricaloverview,wehaveanalyzed thetextbooksofOttavianoFabrizioMossotti(1791-1863),GianAntonioMaggi(1856-1937),PietroBurgatti(1868- 1938) and those of the Peanian tradition (Filiberto Castellano, Cesare Burali-Forti, Roberto Marcolongo, TommasoBoggio).SectionFourisdevotedtothedescriptionofhomographysynthetictheoryinteachingclassical mechanicsintheItalianvectorschool:homographyasanextensionoftheminimum system.Ourconsiderations about the Tullio Levi-Civita and Ugo Amaldi textbook are presented in Section Five. The essential role of the minimum system is evident in our previous analyses. From this, one can develop other concepts (such as the homographies) and introduce new operators. Giovanni Giorgi (1871-1950), a physicist and mathematician emblematicascriticonthetechniquesproposedbythevectorialists,statesBurali-FortiandMarcolongo'smethods are``toocompactanddifficulttoread''.However,accordingtoGiorgi,oneofthemeritsoftheirworkwasthedepth ofthetheoryofvectorhomographies.
Vector calculus in the didactics of mechanics in Italy in the early twentieth century
Dell'Aglio L.
;Freguglia P.
2023-01-01
Abstract
Firstly,wehaveprovidedahistoricaloutlineofthegeometricalcalculusandgeometricalalgebra duringthesecondpartofXIXcenturyandthefirstyearsofXXcentury.Subsequently,ouraimhasbeentohighlight through this period in Italy, and in the international context (comparison with Euge Áne Prouhet (1817-1867), CharlesSturm(1803-1855),GustavRobertKirchhoff(1824-1887),OsipIvanovichSomoff(1815-1876),PaulAppell (1855-1930),OttoFo Èppl(1854-1924)andothers)thedidacticuseofgeometricalcalculus(andofthehomographies) intheuniversitytreatisesofmechanicsandofmathematicalphysics.Inthishistoricaloverview,wehaveanalyzed thetextbooksofOttavianoFabrizioMossotti(1791-1863),GianAntonioMaggi(1856-1937),PietroBurgatti(1868- 1938) and those of the Peanian tradition (Filiberto Castellano, Cesare Burali-Forti, Roberto Marcolongo, TommasoBoggio).SectionFourisdevotedtothedescriptionofhomographysynthetictheoryinteachingclassical mechanicsintheItalianvectorschool:homographyasanextensionoftheminimum system.Ourconsiderations about the Tullio Levi-Civita and Ugo Amaldi textbook are presented in Section Five. The essential role of the minimum system is evident in our previous analyses. From this, one can develop other concepts (such as the homographies) and introduce new operators. Giovanni Giorgi (1871-1950), a physicist and mathematician emblematicascriticonthetechniquesproposedbythevectorialists,statesBurali-FortiandMarcolongo'smethods are``toocompactanddifficulttoread''.However,accordingtoGiorgi,oneofthemeritsoftheirworkwasthedepth ofthetheoryofvectorhomographies.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
