> magisterchessmutt Wrote:
>> However, as to which unit came 1st.
>> and for what objective, I have no way of knowing
>> for certain. It's use in area measurement work
>> would be very handy in right triangle trigonomic
> While I believe the Egyptians knew of √2 and
> that it was formed by the diagonal of a square of
> sides 1 unit, the remen only gives √2 values of
> 10/7 and 7/5, which, while useful on smaller
> projects, are much too crude for large-scale
> projects such as land surveying and pyramid
I do agree with the last part of that and I appreciate anyone stating that.
I suppose this will turn out to be more emphasis on my working premise that this math and metrology began with calendars and counting days (365 / 3 = 121.66666666 = ~100 Remen of 1.216733603 in feet, hence if so the Cubit is very likely descended from the Remen since it otherwise probably takes more work to eke the Cubit value from the "heavens" that way)*, but I work with at least several approximations of sqrt 2 that can be directly derived from values I use for the Venus Orbital Period. Disregarding correct decimal placement,
1 / (225.0000000 x Pi) = 1.414710605 = 2 / 1.413716694 = 2 / (45 x Pi)
1 / (224.8373808 x Pi) = 1.415733839 = 2 / 1.412694928 = 12 / 1.177245771
In my realm these are a strange fact of life and mathematics because the relationships between mathematically ideal forms of metrological units aren't necessarily geometrically ideal, and the sqrt 2 function of course is a function of geometry. One or more important cases in point,
1.718873385 / 1.216733603 = 1.412694924
2.720174976 / 1.216733604 = 2.235637258 = sqrt 5 to .999807376 = ht Cheops pyramid missing apex section / 8 / 10 as I customarily describe the pyramidion or missing section.
Frankly, at the level of exactitude that many work at, I don't really know what's to stop anyone from identifying the Royal Cubit in feet as sqrt 3 itself (I think I've seen several do this) and then perhaps proceed to declare that since this is about the diagonal of a cube with sides of one foot, that this is evidence of ancient use of the modern foot. I could even be more or less among their number myself before I am finished.
* (Mars Orbital Period 686.971 days / 4 = 1.717427500 x 100, 687 / 4 = 1.717500000; Saturn Synodic Period 378.09 days / 22 = 1.718590909 x 100, 378 / 22 = 1.718181818 x 100.
364 / 21 = 17.33333333, 225 / 13 = 17.30769231, 260 / 15 = 17.33333333, but that might be about where that one runs out of steam, and it's already doing the "Mayan thing" of making 364 out of 365 just to have that much homogeneity).
On the other hand, it may also be counterproductive to assume that there was only a singular value for something such as a metrological unit, or a link between metrological units.
Multiple values may also depend on various formulas that someone might choose from, of course.
Since John Michell has come up in this thread, for what it's worth,
Dimensions of Paradise, pages 114 and 116:
"1000 Roman Miles = 4866048 = 3168 x 1536 feet"
Ever since I started working with the math I use, the inner diameter of the Stonehenge sarcen circle has been given as 48.6693441 feet ((sqrt 240) x Pi), or 40 Remens of 1.216733603 ft
For Michell's figure 4866048, 4866048 / 40 = 1.216512 ft x 10^n.
This is the same as the 1.216733603 figure I use to .99981787, even when Michell's data would be considered raw by my usual standards.
On pages 106 and 115 he gives the Roman mile as 48384 = 504 x 96 ft (48384 / 40 = 1.20690); on page 116 he describes 4866048 and related figures as "the longer values" for these units.
While I'm on the subject, I'm always very pleased to read comments like the ones on page 114 about the foot such as "the foot is the medium that shows up the numerical framework behind the values and ratios of the odd units and allows them to be defined accurately in accordance with reason. Although it appears to stand apart from the other units, the foot in is fact the bond that unites them and makes them systematically coherent."
I'm not sure I'd have put it much differently, and I'm not sure I could have put it any better.
I might want to say the same thing about the 5280 foot mile, that it "appears to stand apart from the other units, the foot in is fact the bond that unites them and makes them systematically coherent". I have never been able to directly relate this value to other units in any satisfactory manner, but the 5280 foot value does splendid things with earth measures at a ratio of (metrological unit): mile.
I have some values near to 5280, but I think it's bad enough the way measuring a large pyramid magnifies small discrepancies in metrological units, let alone measuring something as large as a planet. Those near-5280 values seem more like metrological adapters than useful values in themselves.
Edited 2 time(s). Last edit at 23-Nov-19 23:19 by thinkitover.