### Biography

Lluis Antoni Santaló Sors, Spanish-born Argentine geometer (Girona, Catalunya 09 October 1911 – Buenos Aires 22 November 2001)

Regarded internationally as founder of modern integral geometry and one of greatest geometers of the 20^{th} century

Authored over 150 papers

Authored 25 books between them Vectores y Tensores (1961) and Integral Geometry and Geometric Probabilities (1976)

Invited Lecturer, International Congress of Mathematicians (1950)

### ACHIEVEMENTS

With Chern regarded as founder of hyperbolic integral geometry

Introduced kinetic density for sets of geodesies on two-dimensional surfaces

Introduced affine unimodular invariant (1958)

Obtained integral formulas for a two-dimensional Riemannian space of negative constant curvature

Laid the mathematical foundations for the creation of stereology

Introduced convex sets by horospheres

Proposed a definition for absolute total curvatures of a Euclidean space closed subset

Solved the problem of one-dimensional foliations in a Riemann variety

### CONTRIBUTIONS

A new affine invariant plane and solid convex bodies. Math Notae 16:78-91, 1958

Some integral formulas and a definition of q-dimensional area for a set of points. Rev. Univ. Nac. Tucumán 7:271-82, 1950

An affine invariant for convex bodies in n-dimensional space. Portugaliae Math. 8:155-61, 1949

An affine invariant for closed convex plane curves. Math. Notae 8:103-11, 1948

Some integral formulas referring to convex bodies. Rev. Un. Mat. Arg. 12:78-87, 1946

A theorem on conformal mapping. Math. Notae 5:29-40, 1945

An integral formula concerning convex figures. Rev. Uni. Mat. Argentina 8:165-91, 1942

A theorem and an inequality referring to rectificable curves. Amer. J. Math. 63:635-44, 1941

A theorem on sets of parallelepipeds with parallel edges. Publ. Inst. Mat. Univ. Nac. Litoral 2:49-60, 1940

### EPONYMY

Blaschke-Santaló inequality

Blaschke-Chern-Santaló theorem

Santaló bodies

Santaló conjecture on convex sets

Santaló K point

Santaló point of a function

Santaló formula

### LINKS

http://www.fceia.unr.edu.ar/secyt/apuntes/Santalo/Santalo.htm