The Mathematics of Beauty > Timeline > 1882 - Ballard's The Solution of the Pyramid Problem

A British railway engineer, Robert Ballard, saw the pyramids on his way to Australia to become chief engineer of the Australian railways. He watched from a moving train how the relative appearance of the three pyramids on the Giza plateau changed. He concluded that they were used as sighting devices, and wrote a book with the grand title of The Solution of the Pyramid Problem in 1882.     - The eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org.

Ballard noted that the cross-section of the Great Pyramid is two of what we have called Egyptian triangles. He constructs what he called a Star Cheops, which, he says, "... is the geometric emblem of extreme and mean ratio and the symbol of the Egyptian Pyramid Cheops."

To draw a star Cheops:

1. Draw vertical and horizontal axes.
2. Using their intersection as center, draw two circles, radius 1, and radius 1 + .
3. Superscribe a square about the smaller circle. This will be the base of the pyramid,
4. From the point where an axis cuts the outer circle, draw two lines to the corners of the square. The triangle obtained will be one face of the pyramid.
5. Repeat the preceding step for the remaining three faces, getting a four-pointed star. Cut it out.
6. Fold each triangular face up from the base forming the pyramid.

    - Paul Calter, Squaring the Circle

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