The 47th Problem of Euclid

By Wor. David J. Lettelier
for a Public Oration and Lecture

The 47th problem of Euclid (called that because Euclid included it in a book of numbered geometry problems) in which the sides are 3, 4, and 5 — all whole numbers — is also known as “the Egyptian string trick.”

The “trick” is that you take a string and tie knots in it to divide it into 12 divisions, the two ends joining.  (The divisions must be correct and equal or this will not work.)

Then get 3 sticks — thin ones, just strong enough to stick them into soft soil.  Stab one stick in the ground and arrange a knot at the stick, stretch three divisions away from it in any direction and insert the second stick in the ground, then place the third stick so that it falls on the knot between the 4-part and the 5-part division.  This forces the creation of a 3 : 4 : 5 right triangle.  The angle between the 3 units and the 4 units is of necessity a square or right angle.

The ancient Egyptians used the string trick to create right angles when re-measuring their fields after the annual Nile floods washed out boundary markers.  Their skill with this and other surveying methods led to the widely held (but false) belief that the Egyptians invented geometry (geo=earth, metry=measuring).

Thales the Greek supposedly picked the string trick up while traveling in Egypt and took it back to Greece.  Some say that the Greek mathematician and geometer Pythagoras, described in Masonic lectures as “our worthy brother,” also went to Egypt and learned it there on his own.  In any case, it was he who supplied the PROOF that the angle formed by the 3 : 4: 5 triangle is invariably square and perfect.  It is also said that he actually sacrificed a hecatomb, that is a sacrifice of one hundred bulls, which ranked as the highest kind of religious offering, upon completing the proof.

How is this forty-seventh proposition the foundation of all Masonry, and what was the significance of the problem which led to such a demonstration by the ancient philosopher? 

The knowledge contained in this proposition is at the bottom of all systems of measurement and every mechanic at the present day makes use of it consciously or unconsciously, whether it be the land surveyor blocking out a township, or the gardener measuring out his tennis court, or the carpenter calculating the pitch of a roof.  He may not know anything about geometry, but the “rule of thumb” by which he works has been deduced from this proposition.  To the practical builder the knowledge is invaluable, and if we will carry ourselves back in imagination to a time when this knowledge was still unknown, we will realize that its discovery was an event of great importance in the history of architecture, an epoch-making event to be ranked with such modern discoveries as those of the law of gravitation, wireless TV or telephones, and space travel.