question: in 1933 he published a theorem on convex polyhedra and an elementary proof of the existence of a centre of symmetry in a three-dimensional convex polyhedron.
Capitalize this past sentence correctly.
A: In 1933 he published A theorem on convex polyhedra and An elementary proof of the existence of a centre of symmetry in a three-dimensional convex polyhedron.

question: play some of them can be a family.
Capitalize this past sentence correctly.
A: Play some of them can be a family.

question: apart from ponta delgado on the island of sao miguel are the spanish cadiz, charleston on the east coast of the u.s. and the world in two days on the new york city program.
Capitalize this past sentence correctly.
A: Apart from Ponta Delgado on the island of Sao Miguel are the Spanish Cadiz, Charleston on the east coast of the U.S. and the world in two days on the New York City program.