Could such an accurate and elegant relationship be That level of accuracy seems very impressive and is certainly the reason that Taylor's idea has been widely promoted and believed. 04% or better (depending on the data that one uses). An equivalent statement is that the slope of each face of the Great Pyramid is very close to 4/ &pi=1.273239. This relationship is accurate to within. It is true that if one divides the Great Pyramid's perimeter by its height, one indeed obtains a very good approximation to 2 &pi. In more recent times, books such as Secrets of the Great Pyramid by Peter Tompkins discuss the relationship between &pi and the Great Pyramid and also another relationship involving the number φ (the famous Golden Mean) at considerable length, almost seeming to take it for granted that those relationships are really intentional. These ideas wereįurther promulgated and elaborated by Charles Piazzi Smyth - Professor of Astronomy at Edinburgh University and Astronomer Royal of Scotland - in his book Inheritance in the Great Pyramid, published in 1864. Taylor's ideas were presented in his book The Great Pyramid: Why Was It Built? And Who Built It?, published in 1859. He suggested that perhaps the Great Pyramid was intended to be a representation of the spherical Earth, the height corresponding to the radius joining the center of the Earth to the North Pole and the perimeter corresponding to the Earth's circumference at the Equator. He compared this to the fact that if one divides the circumference of aĬircle by its radius, one obtains 2 &pi. He discovered that if one divides the perimeter of the Pyramid by its height, one obtains a close approximation to 2 &pi. It was John Taylor who first proposed the idea that the number &pi might have been intentionally incorporated into the design of the Great Pyramid of Khufu at Giza. But since we're so used to always seeing things either rounded or based on a multiple of 1/2, 1/5, or 1/10, we don't really notice how so many numbers behave like this.Pi and the Great Pyramid PI AND THE GREAT It has to do with the prime factors of the base. That is, if you want to know the k-th digit in the expansion of pi, you simply need to add enough terms (a number of terms dependent on the value of k) of the series together.Īlso, I should add that decimal expansions are a minefield, suitable only for scientists and accountants! In reality, the number of rationals that you can represent with finite, non-repeating expansions is pretty small. If you have an appropriate series which equals pi in the limit, (probably monotonic ones or series which converge "fast enough" in some other sense) you can calculate the digits out perfectly. So, for example, do binary long division on 22/7 = 10110b/111b which would start off 11.001.īetter rational approximations would lead to better binary expansions. If you want to represent pi with arbitrary precision in a base n, the standard way to do it would be to find a rational number very close to pi, and then convert that rational to an n-ary representation. It sounds like you're trying to translate the decimal string directly into binary.
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