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## 'Babylon Numbers' printed from http://nrich.maths.org/

We recieved two very different interpretations of these numbers. Do
theyconvince you?
James and Ryan said that
We think that the numbers are two of a pair of pythagorean triples
$(a, b, c)$, so that

$$

a^2+b^2=c^2

$$

In each case the third number is

$$120, 3456, 4800, 13500, 72, 360, 2700, 960, 600, 6480, 60, 2400,
240, 2700, 90$$

We wondered why these numbers had been picked in this order, but
then found out that they are arranged in order of decreasing angle
of the triangle. So, the first row is a (119, 120, 169) triangle
which has an angle of $45.2^\circ$ and the last but one has an
angle of $33.3^\circ$.

Our hypothesis shows that the errors are in rows 2, 9, 13, 15.
These should read

4825, 11521

541, 481

25921, 161

53, 106

The Babylonians might have used these numbes to help to build
things.

Michael writes suggesting that the numbers
are related to astronomical measurements
The numbers are the measurements of time.

- The number 3541 which is the equivalent of 10 lunar years with
just 2 leap days.
- That leads to 4961 which compares to 14 lunar years.
- The number 8161 is the equivalent of 23 lunar years with 11
leap days.
- Is the 10 in the third row intended as leap days?
- 1771 equates to 5 lunar years.
- The number 2929 is practically identical to 8 solar years at
2922 days.
- That 8 year period is also 13 orbits of Venus.
- It is also 5 orbits of the Synodic cycle at 2920 days.
- 4961 is also 22 orbits of Venus making it a common target with
14 lunar years.
- 18,541 equates to 27 orbits of mars.
- The total of the second column at 57613 equates to 99 synodic
cycles while the totals of the three columns at 116,798 equates to
200 synodic cycles and the totals of column 1 and 3 equates to 101
synodic cycles.
- There are more synodic cycles evident with the addition of
numbers e.g. 2291 + 3541 = 5832 or 10 synodic cycles in 16 years.
(+ the 7 as leap days)
- But what about 1679? It equates exactly to one orbit of the
Asteroids which were only discovered in 1801 with the aid of a
telescope?
- The number 25,921 is just one above the cycle of the Zodiac at
25,920 years, so the numbers are neutral to represent days or years
i.e. = 71 solar years.