**GREAT PYRAMID SHAFT GEOMETRY**

The height of the pyramid is 280 cubits. The midpoint of the height is 140 cubits above ground level. A diagonal on the square of of 140 cubits is 198 cubits. The floor of the king's chamber and the king's chamber passage is 198 cubits below the apex, or 82 cubits above ground level. The horizontal area of the pyramid 82 cubits above ground level is equal to one-half of the horizontal area of the pyramid at ground level.

One half of the 198 cubit distance from the floor of the king's chamber passage to the apex of the pyramid is 99 cubits. The king's chamber shafts exit the pyramid 154 cubits above ground level. At this height above ground level, the horizontal distance between the faces of the pyramid is 198 cubits. The arc in the diagram below is struck from the apex to the mid point of the 198 cubit distance from the apex to the floor of the king's chamber passage. The horizontal area of the pyramid at the height the king's chamber shafts exit the pyramid is equal to one half of the square area of the height of the pyramid.

In the diagram below, the 198 cubit horizontal distance between the exit point of the king's chamber shafts is squared. The diagonal of the square marks the 45 degree angle of the king's chamber southern shaft. The arc from the midpoint of the horzontal distance from the exit points of the shafts marks the length of 99 cubits for the inclined section of the king's chamber southern shaft. Given the 45 degree angle of the southern shaft, the 99 cubit diagonal distance produces a 70 cubit vertical distance below the exit points of the shafts. 154-70 = 84. The roof of the horizontal sections of the king's chamber shafts and the roof of the king's chamber passages are 84 cubits above ground level. The point where the roof of the inclined section of the southern shaft intersects the horizontal section of the shaft is also 70 cubits north of the exit point of the shaft, or 29 cubits south of the vertical midline of the pyramid: 99-70 = 29. The midpoint of the distance from ground level to the 154 cubit height above ground level is 77 cubits above ground level. Extending the 45 degree angle of the southern shaft down to 77 cubits above ground level is also 77 cubits below the exit points of the shafts and 77 cubits north of the exit points, or 22 cubits south of the vertical midline of the pyramid. A line from this point, 77 cubits above ground level and 22 cubits south of the vertical midline of the pyramid, to the exit point of the northern shaft, marks the location of the northern shaft from 84 cubits above ground level to the exit point. This produces a slope of 7/11 for the northern shaft, one half of the 14/11 slope of the outside of the pyramid.

The vertical distance from the floor of the king's chamber to the exit points of the king's chamber shafts is 72 cubits 154-82 = 72. The midpoint of this vertical distance is 36 cubits. The queen's chamber shafts terminate 36 cubits below the exit points of the king's chamber shafts, 118 cubits above ground level 154-36 = 118.. The vertical distance from the bottom of the 198 cubits square to the termination points of the queen's chamber shafts is 162 cubits 198-36 = 162. The mid point of this 162 cubit vertical distance is 37 cubits above ground level 118 - 81 = 37. Lines from the vertical midline of the pyramid, 37 cubits above ground level, to the termination points of the queen's chamber shafts, mark the 9/11 slope of the queen's chamber shafts 81/99 = 9/11. The bottom of the 198 cubit square is 44 cubits below ground level 198 - 154 = 44. The horizontal sections of the queen's chamber shafts are 44 cubits above ground level.

Twice the 44 cubit distance from the bottom of the 198 cubit square marks the 88 cubit sloping distance of the floor of the grand gallery. The sloping distance of the floor of the ascending passage is 72 cubits. The ratio between the floor of the ascending passage and the floor of the grand gallery is 72/88, or 9/11.