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The limestone blocks of the Orion pyramids consist of mostly calcite mineral, whose structure can be triangular and octahedral in various forms. Each of the Giza pyramids is apparently designed as the top half of an octahedron, monumental formations of calcite. The angular mathematics of the Orion pyramidal design will be addressed shortly, but their limestone blocks contain information regarding the construction methods of the pyramid builders.

Research of J. Davidovits into ancient geopolymers has demonstrated through chemical X-ray analysis that the casing stones of the Giza pyramids are synthetic, being of lower density than any quarried stone due to trapped air bubbles and consisting of 85-90% calcite with other exotic mineral constituents like opal CT, hydroxy-apatite and silico-aluminates. CAT-scan work on the core stones have recorded hairs deeply embedded in the matrix of the stone, another clue that the pyramid blocks were cast using liquid stone, though RC14 dating of hair samples contained in the stone have not been reported. This type of test could establish firm construction dates for the stones, though the likelihood of later facade reconstruction is strong. Corroborating evidence for the ancient use of advanced geopolymers comes from Mesopotamia, where the manufacture of basalt has been extensively documented. Note that the synthetic stones are of high piezoelectric crystalline content.

Diverse new technologies have incorporated fractal patterning for signal enhancement, data compression and encryption. Recent acoustic resonance experiments have illuminated a connection between the phi ratio and a nonlinear acoustic standing wave structure. Cervenka, Bednarik and Konicek at the Czech Technical University in Prague have modeled the structure of a nonlinear standing wave excited in a cylindrical resonator. Driven by periodic oscillations a resonant cavity can be stimulated to its fundamental resonant frequency producing both harmonics and subharmonics. When the standing wave is driven into high amplitude the nonlinear effects couple energy from low to high-frequency modes. This increase in harmonics can create a shockwave, diminishing the quality of the resonator dramatically. Multifrequency driving of the resonant cavity has been used to increase the energy storing. If the energy is coupled to lower frequencies, or subharmonics, less acoustic dissipation is observed allowing for a more efficient system. Bednarik describes Resonant Macrosonic Synthesis:

[T]he interactions of acoustic waves at some fixed frequencies without the energy losses in the higher harmonics is of considerable interest in acoustics. Such interaction creates the possibility of direct transformation of coherent sound at the given frequency by sound of another frequency without an electro-magnetic energy source... For a region of three modes with given angular frequencies, if the sum of two of them is equal to the remaining one, the interactions of these modes can be obtained from the nonhomogenous Burgers equation for nonlinear standing waves.

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