Richard C. Hoagland claims “the Face on Mars” (See video below) is part of a city built on Cydonia Planitia consisting of very large pyramids and mounds arranged in a geometric pattern, with the ratios between measured angles roughly equaling mathematical constants such as π (pi), e, and the square root of 2. He states that the ratio between the surface area of a sphere and the surface area of the tetrahedron inscribed within it, 2.720699 (π × square root of 3/2), is an approximation of e that Hoagland refers to as e‘. Since e‘/π (square root of 3 / 2) is −0.866, Hoagland speculates that the primary meaning of the geometry of Cydonia is to emphasize the ratio of the sphere and circumscribed tetrahedron. To Hoagland, this is evidence that an advanced civilization might once have existed on Mars, and that NASA is suppressing the evidence for reasons explained in a Brookings Institution report entitled Proposed Studies on the Implications of Peaceful Space Activities for Human Affairs. In fact, although the report did state that it is a possibility that such information would destabilize society, it did not itself even consider the question of withholding information from the public. The report recommended that the question ought to be studied.

On April 5, 1998, the Mars Global Surveyor probe sent back better images of the Cydonia region that indicated that the face was an irregularly shaped mountain. Hoagland contends these images were run through multiple filters that degraded the original image in quality, giving it a catbox appearance which obscures what is really on Mars. On September 21, 2006, several new 3D views were released, derived from the high-resolution stereo camera on the European Space Agency’s Mars Express orbiter. In response to their publication Hoagland remarked “Science is not about what you can see. It’s about what you can measure,”, and Hoagland’s co-author Mike Bara has accused the European Space Agency, which released that photo set, of fraud. The image from the HiRISE camera on Mars Reconnaissance Orbiter, released in April 2007, was so detailed that even Hoagland appears to have abandoned his contention that the whole structure is a face. In the epilogue to his book released the following October, he analyzes instead the details of the face mesa within the MRO frame that he says are “obviously collapsed geometric ruins [with] parallel walls, multiple 3-D planes, twisted beams, and thin girders.”

In March 2010 the European Space Agency’s Mars Express returned radar and visual data from Mars’ larger moon, Phobos, showing the moon in unprecedented detail. Hoagland wrote that Phobos was revealed to be artificial, a “manufactured” satellite. He added that ESA itself would announce this finding at the European Planetary Science Congress in Rome, in September 2010. The Phobos session at EPSC in fact announced that Phobos is probably formed from re-accretion of orbiting debris.

Hoagland also claims that the true color of Mars is salmon red with patches of greenish plant life and a light blue sky. This runs counter to widely accepted spectrographic observations. He also claims that Mars was once the moon of a larger planet which exploded, leaving Mars isolated, that the advanced civilization on Mars had prior warning of the cataclysm and so escaped via migration to planet Earth, eventually adapting to the environment and becoming the present human race, and that the numerous objects surrounding the landing sites of the Mars Exploration Rovers are in fact pieces of Martian machinery.