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Re: Strange Maths (was Re: Why not 13 months?)
Whittet (Whittet@shore.net)
22 Jul 1995 01:08:58 GMT
In article <dougDC2uDG.EC7@netcom.com>, doug@netcom.com says...
>
>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
So since the base is for each new row of stones is a little smaller than
it was for the last one we laid, do we build a new wheel for each course?
How do you keep the coursing straight as we go up?
How do you get this to give the slope equal to 1 stadium which is equal to
1/600 of the Earths circumference at the equator?
How do you make it come out so the perimeter is 36524"?
It isn't just getting PI, but the combination in the best possible correlation
using unit fractions so we can tell the workmen how to build it.
What I am looking for is the instruction to the workmen, preferably in
unit fractions since ratios like 14:11 were not used by the Egyptians.
>--
>Doug Merritt
Steve
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