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## The Giza Oracle: A New Theory Concerning the Design of the Pyramids of Giza (cont.)By © (2006) Scott Creighton

The problem of finding a mathematical solution to the pyramid alignment puzzle presents itself with little difficulty and utilises what has come to be known as the Giza Centroid Alignment Theory or (CAT). This theory had its origins in considering the puzzle of the very unusual `bisectors' in the pyramids of Khufu and Menkau-Ra (figure 2).

Figure 2 - Ikonos satellite image of the Great Pyramid

The `bisectors' of Khufu and Menkau-Ra are 8 lines (4 in each pyramid) that run vertically through the centre of each face of these 2 pyramids, which are formed by the angled arrangement of the stone blocks. What could these 8 lines mean and why should they be found only on the faces of these 2 pyramids?

A possible and surprisingly simple mathematical answer was quickly discovered. Unlike a square or circle, a triangle that is not equilateral has many centres known as `centroids'. Each of these different centroids or `points' within the triangle satisfies some unique property. Our modern mathematics is aware of over a hundred different triangle centroids but it seems the ancients knew how to plot only the three simplest of these: Incentre, Centroid and Circumcentre. The ancient Greeks, however, added a fourth triangle centroid known as the Orthocentre. The three simplest and most ancient triangle centroids the Designers may have been familiar with are detailed below (figures 2a-2d).

### Centre 1 - The `Incentre'

This point requires a circle to be inscribed within the triangle whereby the perimeter of the circle touches all three sides of the triangle. The centre of the inscribed circle is then plotted and this point becomes the triangle's Incentre.

Figure 2a - `Incentre'

### Centre 2 - The `Centroid'

This point requires a line to be drawn from each of the triangle's vertices to the midpoint of the opposite parallel. The intersection where the lines meet is plotted and this point becomes the triangle's Centroid.

Figure 2b - `Centroid'

### Centre 3 - The `Circumcentre'

This point requires a circle to be circumscribed around the triangle in such a way that its perimeter touches all three vertices of the triangle. The centre of the circumscribed circle is then plotted and this point becomes the triangle's Circumcentre.

Figure 2c - `Circumcentre'

If we now overlay each of the three different centroids outlined above against a site plan of Giza, we arrive at an alignment of the 3 centroids that is a precise match with the centre points of the Giza Pyramids.

Figure 2d - The 3 Centroids align with the Pyramid Centres

Of course, the triangle used in the above example has been very carefully constructed in order to achieve an exact alignment of the 3 centroids with the pyramid centres. Indeed, no other triangle will offer 3 centroids that will exactly align with the pyramid centres. The main point of this design technique, however, is that it provides a possible means of explaining the 8, hitherto, mysterious centre lines of Khufu and Menkau-Ra which correlate precisely with the underlying plan (figure 3a).

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