Written by a distant relative of the more famous author Count Tolstoy, by one of the first Russian science fiction writers, this tells the story of a mad scientist who tries to take over the world, only to be stopped by the superior goodness of his proletarian workers.

Mathematical content is limited to an explicit description of the parabolic focussing that makes the death ray work. There are no hyperboloids involved.

"Engineer Garin" is an allusion to Russian writer and engineer Garin-Mikhailovskii.

The mathematical (physics actually) theory behind Garins "Death Ray" is not practical. The hyperbolids don't collect light into a focal point, it's the paraboloids (parabolic reflectors for example).

Science aside the book is excellent and the main character Garin has indeed a captivating persona. Taking account the time of the writing of the book, it is quite safe to say it is a genre-defining piece of literature.

The only downside of the book is unrealisticly positive "hero" and the overall idea of proletariat revolution. But then again it was written in the Soviet Union.

An estonian band Vennaskond has a song titled "Engineer Garin's Hyperboloid". In that song (as in the book by my mind) the Hyperboloid is the embodiment of desire, desperation and ambition, Garin and main female character Zoya the ultimate gamblers. You may not like them or their goal, but you just got to respect a man trying to control the world:)