This video comes from a series of parapsychological experiments performed by The DHARMA Initiative.

As in Arthur C. Clarke's "The Nine Billion Names of God" (1953), mathematics can provide a shortcut to the Day of Judgement. But... is it worthwhile?

Based on an idea of Mariano Tomatis, this geometrical puzzle is the mix of two popular puzzles: Sam Loyd's Get off the Earth (1896) and Paul Curry's Missing Square Puzzle. The skulls and the geometry have been created by Gianni Sarcone.

The first example of vanishing area puzzles was reported in the book Libro d'Architettura Primo by Sebastiano Serlio (1475-1554), an Italian architect of the Renaissance. Greg Frederickson (1) credits Serlio with one of the variants that transformed the same 3×10 rectangle into a 4×7 and 1×3 rectangles. Curiously, as Prof. David Singmaster has observed, Serlio has been solving a practical problem of converting one rectangle into another and has NOT noticed that the two had different areas!

Sebastiano Serlio, Libro d'Architettura Primo, 1566, p.16

The first description and mathematical explanation of the vanish paradox was found in a math puzzle book with a very long title: Rational Recreations: In which the Principles of Numbers and Natural Philosophy are Clearly and Copiously Elucidated, by a Series of Easy, Entertaining, Interesting Experiments. Among which are All Those Commonly Performed with the Cards, L. Davis; J. Robson; B. Law; and G. Robinson, 1774 by William Hooper. Probably Hooper cribbed the puzzle from the book Nouvelles récréations physiques et mathématiques by the French author Edmé Gilles Guyot (1770).(2) See here or download a PDF of William Hooper's pages.

Italian subtitles courtesy by Enzo Valenzetti’s heirs

Notes

(1) Greg N. Frederickson, Dissections: Plane and Fancy, Cambridge University Press, 1997, pp.271-273.

(2) Gianni Sarcone, Puzzillusions, Archimedes-lab.org, Carlton Books Ltd, ISBN 1844420647.