Margherita Piazzola Beloch

Margherita Piazzolla Beloch (July 12, 1879 in Frascati – 1976 in Rome) was an Italian mathematician who worked in algebraic geometry, algebraic topology and photogrammetry.

Biography

Margherita was the daughter of the German historian Karl Julius Beloch, who taught ancient history for 50 years at Sapienza University of Rome, and American Bella Bailey. Margherita studied mathematics at the Sapienza University of Rome and wrote her undergraduate thesis under the supervision of Guido Castelnuovo. She received her degree in 1908 with Lauude and "dignita' di stampa" which means that her work was worthy of publication and in fact her thesis "Sulle trasformazioni birazionali dello spazio" (On spacial birational trasfomation) was published in the Annali di Matematica Pura ed Applicata. Guido Castelnuovo was very impressed with her talent and offer her the position of assistant which Margherita took and held until 1919, when she moved to Pavia and the successive year to Palermo to work under Michele De Franchis, under very important figure of the Italian school of algebraic geometry of those days. In 1924, Beloch completed her "libera docenza" (a degree that at that time had to be obtained before one could become a professor) and three years later she become full professor at the University of Ferrara where she taught until her retirement (1955).

Scientific Work

Her main scientific interest were algebraic geometry, algebraic topology and photogrammetry. After her thesis she worked on classification of algebraic surfaces studying the configurations of lines that could lie on surfaces. The next step was to study rational curves lying on surfaces and in this framework Beloch obtained the following important result[1]

Hyperelleptic surfaces of rank 2 are characterised by having 16 rational curves

Beloch also made some contribution to the theory of skew algebraic curves.[2] She kept working on topological property of algebraic curves either planar or lying on ruled or cubic surfaces for most of her life writing about a dozen papers on these subjects[3]

Around 1940 Beloch become more and more interested in photogrammetry and the application of mathematics, and in particular algebraic geometry, to it. She is also known for her contribution to mathematics of paper folding:[4] In particular she seems to be the first to formalised an origami move which allow, when possible, to construct by paper folding the common tangents to two parabolas. As consequence she showed how to extract cubic roots by paper folding[5] something that is impossible to do by rule and compass.

References

Margherita Piazzola Beloch at the Mathematics Genealogy Project

  1. ↑ Strickland E. Scienziate d'Italia: diciannove vite per la ricerca.
  2. ↑ M. Beloch Piazzolla, Sur le nombre des plurisecantes et sur la classification des courbes gauches algebriques, Comptes Rendus de l'Ac. des Sciences , 1940
  3. ↑ http://math.unipa.it/~brig/sds/prima%20pagina/tirocinio/Beloch%20Margherita%20biblio.htm
  4. ↑ Hull, Thomas C. Solving cubics with creases: the work of Beloch and Lill. Amer. Math. Monthly 118 (2011), no. 4, 307-315.
  5. ↑ M. Beloch Piazzolla, Sul metodo del ripiegamento della carta per la risoluzione dei problemi geometrici, Periodico di Mathematiche Ser. 4, 16 (1936) 104–108.


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