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July 6, 2020, 5:27 am UTC    
March 04, 2020 07:38AM
keeperzz Wrote:
-------------------------------------------------------
> Hi Kanga,
>
> What is 280c diagonal? Could you create simple drawing?
>
> Alex.

Sorry, I don't know how to post an image.

Just know this. At the 154c level (top of course 104), the horizontal length is 198c cubits. The square at this level has a diagonal of 198c x rt2 = 280c. That is, they knew 280/198 (or 140/99) as a rational approximation to rt2.

They then used this value of rt2 and applied it to the height to make the half-area level, the level of the King's Chamber floor (at elevation 82c, since 82c = 280c - 198c). (Sorry, again no visual.)

Or think of it this way. The KC floor has an elevation of 82c, which means that if a new pyramid were built at this level, its height would be 198c. But 198 stands in relation to 280 as 1:rt2. In other words, this new pyramid is a 1/rt2 scaled down version of the compete pyramid, which means its new base level is 1/rt2 times the base length of the complete pyramid, which means the base of the new pyramid has half the area (1/rt2 squared = 1/2) of the complete pyramid... hence the half-area level.

The 82c level shows how 198 and 280 are related arithmetically, while the 154c level shows how 198 and 280 are related geometrically.
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