Please Note: The quotations below and on the linked page (The Proof of Archytus)
are reproduced with permission from Dover Publications, 31 East 2nd Street, Mineola NY 11501. The
Dover edition of the book mentioned immediately below, was first published in 1981, and is an
unabridged republication of the work first published in 1921 by the Clarendon Press, Oxford. The
errata of the first edition have been corrected.
At the end of his preface to A History of Greek Mathematics, Sir Thomas Heath makes the following remark:
" The work was begun in 1913, but the bulk of it was written, as a distraction, during the first three years of the war, the hideous course of which seemed day by day to enforce the profound truth conveyed in the answer of Plato to the Delians. When they consulted him on the problem set them by the Oracle, namely that of duplicating the cube, he replied, 'It must be supposed, not that the god specially wished this problem solved, but that he would have the Greeks desist from war and wickedness and cultivate the Muses, so that, their passions being assuaged by philosophy and mathematics, they might live in innocent and mutually helpful intercourse with one another.'
Greece and her foundations are
Built below the tide of war,
Based on the crystalline sea
Of thought and its eternity.
Since this remark contains so much from which the world could profit today, I decided to put it on a Web page.
This remark also prompted me to turn, in Heath's work, to the discussion of the above mentioned problem. I found there that the solution of Archytus involves three surfaces--torus, cylinder, and cone. Since all three of these surfaces have been subjects of projects for me, I could not resist the temptation to illustrate The Proof of Archytas.