sides were in a 3–4–5 ratio. They were able to estimate the area of a circle by subtracting one-ninth from its diameter and squaring the result: Area ≈ [()D]2 = ()r2 ≈ 3.16r2, a reasonable approximation of the formula . The golden ratio seems to be reflected in many Egyptian constructions, including the pyramids, but its use may have been an unintended consequence of the ancient Egyptian practice of combining the use of knotted ropes with an intuitive sense of proportion and harmony. Population Estimates of the size of the population range from 1–1.5 million in the 3rd millennium BC to possibly 2–3 million by the 1st millennium BC, before growing significantly towards the end of that millennium. DNA In 2012, the DNA of the 20th dynasty mummies of Ramesses III and another mummy believed to be Ramesses III's son Pentawer were analyzed by Albert Zink, Yehia Z Gad and a team of researchers under Zahi Hawass, then Secretary General of the Supreme Council of Antiquities, Egypt. Genetic kinship analyses revealed identical haplotypes in both mummies. Using the Whit Athey's haplogroup predictor, they identified the Y chromosomal haplogroup E1b1a (E-M2). In 2017, a team led by researchers from the University of Tuebingen and the Max Planck Institute for the Science of Human History in Jena tested the maternal DNA (mitochondrial) of 90 mummies from Abusir el-Meleq in northern Egypt (near Cairo), which was the first reliable data using high-throughput DNA sequencing methods. Additionally, three of the mummies were also analyzed for Y-DNA. Two were assigned to West Asian J and one to haplogroup E1b1b1 both common in North Africa. The researchers cautioned that the affinities of the examined ancient Egyptian specimens may not be representative of those of all ancient Egyptians since they were from a single archaeological site. Whilst not conclusive since the few relatively older mummies only go back to the 18th–19th dynasty, the rest being from then up to late Roman period, the authors of this study said the Abusir el-Meleq mummies "closely resembled ancient and modern Near Eastern populations, especially those in the Levant." The genetics of the mummies remained remarkably consistent within this range even as different powers—including Nubians, Greeks, and Romans—conquered the empire." A wide range of mtDNA haplogroups were found including clades of J, U, H, HV, M, R0, R2, K, T, L, I, N, X, W. The authors of the study noted