The Great Pyramid of Giza, which the ancient Egyptians called Akhet Khufu, 'The Horizon of Khufu,' stands 481 feet tall, holds about 2.3 million stone blocks weighing 2.5 to 80 tons each, and covers a 13-acre base. It was the tallest structure on Earth for 3,800 years. None of that is the puzzle. The puzzle is the precision. The base is level to within 2.1 centimeters all the way around its 755-foot edge, an error of less than an inch across 13 acres. The four sides point to true north, south, east, and west to within 3/60ths of a degree. The average error in that alignment is 0.06 degrees, tighter than the best modern surveyors manage with GPS and lasers. Sir Flinders Petrie, a British survey engineer who spent two years measuring the pyramid in 1880-82, called the precision 'extraordinary' and recorded corner sockets cut accurately to within half an inch across a 750-foot diagonal.
The pyramid is also a stunning piece of built-in mathematics. Divide its perimeter by its height (1,760 royal cubits over 280) and you get 2π to four decimal places. It captures the value of pi in stone centuries before the Greek mathematician Archimedes is credited with working out a close approximation. The ratio of the pyramid's height to its base also comes out to a near-perfect golden ratio, φ (1.618...). And the base perimeter of 1,760 royal cubits, multiplied by 100, equals 176,000, the circumference of the Earth in miles, to within 0.2 percent. Whether these are deliberate or amazing coincidences has been argued for two hundred years. What no one can argue is that they are there.
The Great Pyramid has narrow shafts running from the King's Chamber and Queen's Chamber out to the surface, and they point at specific stars as they stood when the pyramid was built, around 2,560 BCE. The southern shaft of the King's Chamber aimed straight at Orion's Belt, at the star Al Nitak, as it crossed the sky's midline around 2,500 BCE. The northern shaft pointed at the star Thuban in Draco, which was then the pole star. Robert Bauval's 1983 Orion Correlation Theory suggested that the layout of the three Giza pyramids mirrors the three stars of Orion's Belt in their positions and sizes, with the slight offset of the third pyramid matching the slight offset of the star Mintaka from the belt's centerline. And the Nile sits next to the pyramids the way the Milky Way sits next to Orion.
The inner chambers pose engineering problems that modern study still has not solved. The King's Chamber is lined with 100 granite blocks weighing 25 to 80 tons each, hauled from the quarry at Aswan, 500 miles south. Above it sit five stacked 'relieving chambers,' each holding granite beams of up to 70 tons, built to spread the pyramid's weight overhead. The lowest beam has a crack running its full length, not from failing, but from the load it has carried successfully for 4,500 years. When you strike the King's Chamber, it rings at about 438 Hz, within one hertz of the musical note A4, a fact engineers have measured but not explained. The chamber was either perfect by accident or tuned on purpose.
In 2008, engineer Peter Tompkins and physicist Christopher Dunn published work arguing that the standard explanation, that tens of thousands of workers built the pyramid with copper tools, wooden sledges, and earthen ramps, cannot account for the precision. Dunn, a master machinist from aerospace manufacturing, pointed out that the inner passages show tool marks that look like fixed-point machine work, not hand-chiseling: steady depth, even curves, no slips. His 1998 book 'The Giza Power Plant' argued the structure was engineered as a resonance machine, not a tomb. Mainstream Egyptologists reject his conclusions, but they have not shown, in a repeatable way, how the measured tolerances were reached with Bronze Age tools.