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Hi everybody.

In contrast to Egypt, two rivers: Tygrys and Eufrat in Mesopotamia (today's Iraq), were a place of very turbulent history. Rich in water and fertile soil, highly developed cities - attracted conquerors and surprisingly regularly, at intervals of several hundred years, fell victim to another invasion. Sumerians, Akkadians, Amorites (Hammurabi he was an Amorite and it was a period of great prosperity of the local culture), Kassites, Assyrians and others conquered this affluent country. They took over its high culture, and after some time they shared the fate of their predecessors . It is amazing that in these conditions, in spite of the turbulent political history, a highly developed culture has been created that has maintained its continuity and is called Babylonian.


One very important solution was used in Mesopotamia - zero not known in Egypt, either in Greece or in Rome. The circle symbol was used to write the appropriate number of zeros.
The Babylonians used their accounting skills for two purposes, in matters of everyday life (mainly commercial) and astronomy (planetary movement, in eclipses solar and moon).

In the following centuries, the ancient Egyptians also used factions, but mainly factions, which are now called straight fractions, i.e. Form ⅟n. Almost all Egyptian arithmetic was an attempt to spread any fraction (except ⅔) into the sum of simple fractions. Such distribution is not unambiguous. The extension of the system to write fractions was an outstanding achievement of the Babylonians, the meaning of which is confirmed by the difference between Babylonian and Egyptian mathematics. The computational difficulties of the Egyptians did not allow them to cross the barrier of simple bills, and their astronomy did not go beyond simple observations. On the other hand, the Babylonians, with a system allowing for easy counting on integers as well as on fractions, created highly developed astronomy and algebra.

The most amazing aspect of the mathematical abilities of the Babylonians was the computation tables they invented. In 1854, two such tables, dated to about 2000 BC, were found in Senkerah on the Euphrates. They are given squares of numbers from 1 to 59 and cubes of numbers from 1 to 32.

Finally, the question arises: why do the Babylonians use a six-digit number system? There are different theories on this subject and it is difficult to discuss them all here. Neugebauer's theory seems convincing because he thinks that the original number system of the Babylonians was a decimal system. However, after the conquest of the Sumerians it was modified,that we could use the Sumerian system of measures and weights, which divided by 3. We know that the Sumerians were using 1/3 and 2/3 factions.

Currently, fractions have their place in number theory and are subjected to very diverse analysis. For example, they were searched the shortest distribution of the number 1 to the sum of straight fractions (i.e. on the numerator 1) with odd denominators (⅟₁ does not count). Such a distribution was found in 1971 and it has a form 231.
1=1/2+1/5+1/7+1/9+1/11+1/13+1/15+1/35+1/45+1/231


Another theory assumes that this system was taken from the Sumerians, for which the equilateral triangle was the basic figure used in the construction, and the angle in such a triangle is 60 degrees.
There are also theories that see the relationship of a six-digit numerical system with astronomical observations of the ancients. The authors of these theories suggest that the number 60 is the result of multiplying the number of syderic and tropical months.

[(27 * 30) ^ 2] / 810 = 810
810 / 1.111111111111111 (ratio)

30 (month tropical) / 27 (month sideral) = 1,111111111111111 (ratio)
10/9 = 1.111111111111111
30 (month tropical)*9=270 days
27(month sideral)*10=270 days
270 days*86400=23328000
360 (perfect tropical year)*86400=31104000
31104000/23328000=1,333333333333333
1,333333333333333*10(unit of measure)=13,33333333333333

13,33333333333333/1.111111111111111 (ratio)=12
30 (month tropical)*12=360(perfect tropical year)

360(perfect tropical year)*86400=31104000



360(perfect tropical year)*/13,33333333333333=27(month sideral)
364,5 (tropical year) / 13,5=27(month sideral)
31500000(tropical year)/364,5 (tropical year)=86419,75308641975
86419,75308641975-86400=19,75308641975
19,75308641975*360(perfect tropical year)=7111,11111111
7111,11111111/1000(unit of measure)=7,11111111111
7,11111111111*50=355,5555555555
7,2*50=360
7,29*50=364,5
0,29*60=17,4
7,291666666666666*50=364,5833333333333
0,291666666666666*60=17,5

30 (month tropical) * 12 = 360 (perfect tropical year)

360 (perfect tropical year) / 1,111111111111111 (ratio) = 324
360 (perfect tropical year) * 1,111111111111111 (ratio) = 400

(324 * 400) / 360 = 360

129600/27 (month sideral) = 4800
4800 / 13.5 = 355.5555555555556


129600/30 (month tropical) = 4320
4320/12 = 360


355.5555555555556 / 360 = 0.9876543209876544
360 / 1.0125 = 355.5555555555556

360 (perfect tropical year) * 1,0125 = 364.5 (year tropical)


355.5555555555556 * 87480 = 31104000
86400 * 360 = 31,104,000
364.5 * 86400 = 31492800

I do not speak English, that's why I use a google translator. I hope that in time this will be more accurate.Greetings to all of you from Poland.



Edited 1 time(s). Last edit at 19-Jul-18 02:34 by rodz111.

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