Saturday, 16 June 2007

THE FOUR FACES OF KHUFU

Four Golden Rectangles, with diagonals.
Cut along diagonals, stick together adjacent against adjacent, to make four faces


Stick four faces together, add a suitable covering, et voila! The Great Pyramid.


GEOMETRIC THOUGHT FOR THE DAY









The reason why the Great Pyramid is such a harmonious form is more readily apparent when considering the faces than the cross section, for these are derived directly from the Golden Rectangle.

Cut this rectangle into two along the diagonal, creating two right-angle triangles. Put these two together again with the medium-lengthed sides touching. And there it is. You have one of the faces.

Repeat this another three times, then put the four faces together, the long sides on the ground forming a square and the other sides touching, and you have the 3D form of the Great Pyramid.


Obviously, from a practical point of view, if you actually tried to do the above you'd be attempting to stick edges against edges, which is fiddly. You would of course be able to find other easy ways to achieve the same mathematical result but which involve leaving folded flaps useful for sticking.

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