First Published on 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.

Fig1 Copy of RobinsThreeTriangles

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.