In 1859, the pyramidologist John Taylor misinterpreted Herodotus () as indicating that the Great Pyramid's height squared equals the area of one of its face triangles. This led Taylor to claim that, in the Great Pyramid, the golden ratio is represented by the ratio of the length of the face (the slope height, inclined at an angle θ to the ground) to half the length of the side of the square base (equivalent to the secant of the angle θ). The above two lengths are about and , respectively. The ratio of these lengths is the golden ratio, accurate to more digits than either of the original measurements. Similarly, Howard Vyse reported the great pyramid height , and half-base , yielding 1.6189 for the ratio of slant height to half-base, again more accurate than the data variability.