Re: Strange Maths (was Re: Why not 13 months?)
Doug Merritt (doug@netcom.com)
Fri, 21 Jul 1995 17:39:16 GMT
In article <3uodi4$7bi@insosf1.netins.net> DND@netins.net (Alan Hughes) writes:
>The theory was that they used a wheel to measure the length of the sides
>of the pyramid. It is more accurate and repeatable than using a length of
>twine, rope, etc. For a pyramid of height 100 units, take a wheel of
>diameter 1 unit and measure off 100 revolutions of the wheel for the
>side. This gives you a length to height ratio of pi.
To be specific, especially since Whittet@shore.net challenged:
>You have all the answers Paul, tell me how you would instruct the workmen
>to achieve a straight slope of 51d 51'.
Take the pyramid height to be 100 units and the wheel to be 1/2 unit
in diamater. Then its circumference is pi/4. Now measure out 100
rotations of the circle from the center of the pyramid, giving
a triangle with base y = (100*pi/4) and height 100. The hypotenuse
is then
r = sqrt( (100*pi/4)^2 + 100^2)
r = sqrt( 6168.5 + 10000 )
r = 127.155
The angle formed by the hypotenuse and the base is
sin theta = y/r
sin theta = 100/127.155
sin theta = 0.7864
theta = 51.85 degrees
theta = 51 degrees 51 minutes
Ta-da. Simple, and easily within reach of Egyptian technology. All
they have to do is measure 100 units for the height and 100 rotations
of the wheel for the base. (Obviously one gets the same answer no
matter whether this number is 100 or 55 or 723, as long as it's
the same for the height and base.)
Doug
--
Doug Merritt doug@netcom.com
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