Luis Santaló | |
|---|---|
 | |
| Born | Luís Antoni Santaló Sors (1911-10-09)October 9, 1911 |
| Died | November 22, 2001(2001-11-22) (aged 90) |
| Alma mater | University of Hamburg |
| Known for | Blaschke–Santaló inequality |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Buenos Aires |
| Doctoral advisor | Wilhelm Blaschke Pedro Pineda |
Luís Antoni Santaló Sors (October 9, 1911 – November 22, 2001) was a Spanishmathematician.
He graduated from theUniversity of Madrid and he studied at theUniversity of Hamburg, where he received his Ph.D. in 1936. His advisor wasWilhelm Blaschke. Because of theSpanish Civil War, he moved to Argentina as aprofessor in theNational University of the Littoral,National University of La Plata andUniversity of Buenos Aires.
His work with Blaschke onconvex sets[1] is now cited in its connection withMahler volume. Blaschke and Santaló also collaborated onintegral geometry. Santaló wrotetextbooks in Spanish onnon-Euclidean geometry,projective geometry, andtensors.
Luis Santaló published in both English and Spanish:
Chapter I. Metric integral geometry of the plane including densities and theisoperimetric inequality. Ch. II. Integral geometry on surfaces includingBlaschke's formula and the isoperimetric inequality on surfaces of constant curvature. Ch. III. General integral geometry:Lie groups on the plane: central-affine, unimodular affine, projective groups.
I. The Elements of Euclid II. Non-Euclidean geometriesIII., IV.Projective geometry andconics
V, VI, VII.Hyperbolic geometry: graphic properties, angles and distances, areas and curves.(This text develops theKlein model, the earliest instance of a model.)
VIII. Other models of non-Euclidean geometry
A curious feature of this book on projective geometry is the opening onabstract algebra includinglaws of composition,group theory,ring theory,fields,finite fields,vector spaces andlinear mapping. These seven introductory sections onalgebraic structures provide an enhanced vocabulary for the treatment of 15 classical topics of projective geometry. Furthermore, sections (14) projectivities with non-commutative fields, (22) quadrics over non-commutative fields, and (26)finite geometries embellish the classical study. The usual topics are covered such as (4)Fundamental theorem of projective geometry, (11)projective plane, (12)cross-ratio, (13)harmonic quadruples, (18)pole and polar, (21)Klein model ofnon-Euclidean geometry, (22–4)quadrics. Serious and coordinated study of this text is invited by 240exercises at the end of 25 sections, with solutions on pages 347–65.
Amplifies and extends the 1953 text. For instance, in Chapter 19, he notes “Trends in Integral Geometry” and includes “The integral geometry ofGelfand” (p. 345) which involves inverting theRadon transform.[2]
Includes standard vector algebra,vector analysis, introduction totensor fields andRiemannian manifolds,geodesic curves,curvature tensor andgeneral relativity toSchwarzschild metric. Exercises distributed at an average rate of ten per section enhance the 36 instructional sections. Solutions are found on pages 343–64.
