## Numbers and Ratios

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37 is a remarkable number for many reasons but for our purposes the astronomical utility and its connections, as an invariant, to anciently developed concepts involving it are highlighted. The number within mathematics can be studied at https://en.wikipedia.org/wiki/37_(number).

### Astronomy

We have observed in a number of articles (click on tab 37 above to view them), that the number 37 is

- The approximate number of lunar months in three solar years.
- The length of three Saturnian years, of 364 days each, equals 37 lunar months.
- The counting of 37 lunar months six times can generate 222 lunar months, one short of the 223 in the Saros eclipse period and 13 short of the 235 in the Metonic periods anniversary of sun, moon and stars.
- Two lunar years of 12 lunar months could and were alternated with a lunar year of 13 lunar months to achieve 37 lunar months.

#### 3. The counting of 37 lunar months to count Saros and Metonic periods

In the late 1990s I drew a pattern of counting which shows the whole idea without reference to any ancient monument. A scane of this is below:

*Figure 3.1 of a drawing made in late 1990s of the idea of counting sixe sets of 37 lunar months as 12 + 13 + 12 lunar month years equalling 222 lunar months*