> > I wonder the way it spread to the world. It is unlikely that Greeks
> > (Byzantine?) were the first to utilize it, though.
>
> Yes, the Greks were amongst the first to use it in practical mathematics as
> well as
> astro calculations. Even the word ALGEBRA has its root in Arabic.
> However, these werent put to "paractical" use until the Greeks measured the
> Earth's
> diamter and circumference a few thousand years ago.
> The Byzantine empire had nothing to do with it.
To make the story short, Al Kharizmi lived in 770 - 840 AD.
Surprise.. surprise...!
The numbers and some representations existed way before a specific "0".
So, it is odd to associate the utilization of "0" with Greek scientists.
It is interesting that many ancient scientists found precise geometric
numbers and measurements, possibly due to their strong "counting" and
"size understanding" capabilities. Of course, they need a representation
of the numbers, but perhaps not in the decimal system of today. So, the
calculations were probably not performed this way:
110 934.04
22 78.982
X___ +_______
220 1013.022
220
+____
2420
In some sense, what the ancient Greek scientists did resembles the
German optical lens designs prior to the computer aided optical design
tools. It needs a strong intuition and physical understanding. (It's an
art!)
Going on about the optical design, what is the difference between two
design forms of a single focal length lens, one designed for maximum
sharpnes (lppmm), one for maximum contrast between the line pairs? Does
one of the designs need a compromise for the other? What is the "plastic
look" of the pictures taken with 50/3.5 macro? I have the feeling that it
achieved a very nice contrast behavior without much compromise of
resolution.
All the best,
OMer
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