## Geometry

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*First Published on MatrixOfCreation.co.uk in Thursday, 24 May 2012 14:22 where it was read 362 times*

In working at *Lochmariaquer*, an early discovery has returned in the form of a near-Pythagorean triangle with sides 18, 19 and 6. But first, how did this work on cosmic N:N+1 triangles get started?

Robin's earliest work couched the **Lunation Triangle** within three right angled triangles that could easily be constructred yet describe **the number of lunar months and orbits in the solar year** and **the length of the eclipse year**, using the number series 11, 12, 13, 14 to form N:N+1 triangles. Each triangle could then have an intermediate hypotenuse set at the 3:2 point of the shortest side, so as to form the eclipse year (11.37 mean solar months) and solar year (12.368 in lunar months), plus the orbits in a solar year (13.368 orbits). The 12 length is **the lunar months in a lunar year** but also **the mean solar months in a solar year** and the length 13 is **the length of another type of lunar year** (in lunar months) and **the number of orbits in a 12 month lunar year**. A bit of a mouthful so I have made a diagram of them below in figure 1.

*Figure 1 Robin Heath's original set of three right angled triangles that exploit the 3:2 points to make intermediate hypotenuses so as to achieve numerically accurate time lengths in units of lunar or solar months and lunar orbits.*