The Great Pyramid

Abstract

I HAVE been reading in Mr. Piazzi Smyth's book on this subject (“Our Inheritance,” &c.). From the measurements made or cited by the author it appears tolerably clear that if the vertical height of the pyramid, as originally built, be taken as I; the total length of the four base lines will be twice 3.14159, &c., the number which expresses the circumference of a circle whose diameter is I. At first sight this statement seems startling, but I think it may readily be acceded to, and that neither Mr. P. Smyth nor anyone need believe that by inspiration or otherwise, the architect knew the above relation of diameter to circumference, or was a circle-squarer in any special sense. I conceive the architect to have done something like the following:—Deciding first upon the vertical height of his intended pyramid, he took a cord, equal in length to that vertical height, and with it as a radius described a circle on level ground. Along the circumference of this circle he laid another cord, the ends of which met and were fastened together. The circle being thus formed, he drove four pegs, at equal distances inside the cord, so as to stretch it out into a square. The square thus formed gave the lines for the base of the pyramid; and it is obvious that thus the ratio of diameter to circumference would necessarily be built into the pyramid, however ignorant the architect might be. Working drawings (actual size) of surfaces, angles, chambers, passages, and other things would easily be laid out on that ground. The dimensions of the so-called King's chamber, and of a coffer or stone chest therein, which appear to involve the above ratio of 1 to 3.14159, &c., were, I think, arrived at by a somewhat similar process of construction.