Basic Geometry

[Robert]

The whole driving thesis of this novel is geometry: perfect equilateral triangle, parallels to the axis of rotation of the Earth and the Earth’s equator, prime number relationship to the Earth’s circumference.

Why, then, does Mr. Kalfus play fast and loose with basic geometry in his illustrations and his descriptions?

Page 42 (First U.S. Edition 2013) contains a diagram purporting to show “the next great Figure, a Circle”. The circle is to be tangent to the equilateral triangle and its bisecting Line CD, with a diameter equal to each of the Equilateral’s sides. However, if the diameter is indeed equal to the triangle’s sides, the only position for the lower point of tangency must be Point A itself, and the top of the circle will lie above Point C, not below it, as in the diagram. The unmentioned line CH would have an upward slope, not a downward one as in the diagram. (‘Up’ and ‘down’ relate to the diagram on the page, not to the figure laid out in the desert.) Not incorrect, but misleading.

Page 78, however, contains what appears to be a sloppy mistake. Illustrating the use of the compass found in the buried pyramid, Professor Thayer describes the construction of an equilateral triangle using two circles scribed on a line segment. But, he states, “each circle (has) the same diameter as the segment.” The accompanying diagram on page 79 clearly shows that the two circles each have a radius equal to the line segment, not a diameter. If the circles each had a diameter equal to the segment, they would not overlap, but be tangent to each other at the midpoint of the segment.

Not critical to the story, but surprising given the heavy dependence on accuracy to the guiding plot line of precise mathematical communication with Martian astronomer/geometer observers.