 The "hyperboloid" in its title is not a geometrical surface (though it is utilized in the device design) but a "death ray"-laser-like device (thought up by the author many decades before lasers were invented) that the protagonist, engineer Garin, used to fight his enemies and try to become the dictator of the world.The idea of a "death ray" (popularized in "The War of the Worlds" by H. G. Wells, among others) was commonplace in science fiction of the time, but Tolstoy's version is unique for its level of technical details.