Search

The article reports on John Wallis' attribution of the startling fact that a hole can be cut in one of two equal cubes large enough to permit that passage of the second cube to Prince Rupert. It has been showed in 1968 that a hole can be cut in one of two equal regular tetrahedra large enough to permit the passage of the second tetrahedron. A more precise notion of "plug" is considered. It shows that every such stopper has the Rupert property. An argument which shows generally that it is possible to cut a hole in any universal stopper through which every other multipurpose plug of the same diameter can be passed is presented.

The article examines geometrical problems encountered in locating or determining the normals to a parabola and the real roots of a cubic. In the book "Tractatus duo, prior de cycloide, posterior de cissoide," John Wallis made the first rectification of a algebraic curve. The transformation of any cubic equation through the horizontal translation do not alter the number of real roots of the equation. Key information about the Neil's parabola and envelope of the family of normals is further presented.

A review of the article "John Wallis and the French: His Quarrels with Fermat, Pascal, Dulaurens, and Descartes" by Jacqueline Stedall, which appeared in a 2012 issue of the periodical "Historia Mathematica", is presented.