Though megalithic astronomers could look at the
sky, their measurement methods were only accurate using horizon events. Horizon
observations of solstice sunrise/set each year, lunar extreme moonrises or settings
(over 18.6 years) allowed them to establish the geometrical ratios between
these and other time periods, including the eclipse cycles. In contrast, the
synod of Jupiter is measured between its loops in the sky, upon the backdrop of
stars, in which Jupiter heads backwards each year as the earth passes between
itself and the Sun. That is, Jupiter goes *retrograde* relative to
general planetary direction towards the east. Since such retrograde movement
occurs over 120 days, Jupiter will set 120 times whilst moving retrograde. This
allowed megalithic astronomy to study the retrograde Jupiter, but only when the
moon is conjunct with Jupiter in the night sky and hence will set with Jupiter
at its own setting.

# Category: Geometry

## Story of Three Similar Triangles

*first published on 24 May 2012*

Interpreting *Lochmariaquer *in 2012, an early discovery was of a near-Pythagorean triangle with sides 18, 19 and 6. This year I found that triangle as between the start of the Erdevan Alignments near Carnac. But how did this work on cosmic N:N+1 triangles get started?

Robin Heath’s earliest work, *A Key to Stonehenge* (1993) placed his **Lunation Triangle** within a sequence of three right-angled triangles which could easily be constructed using one megalithic yard per lunar month. These would then have been useful in generating some key lengths proportional to the lunar year:

**the number of lunar months in the solar year,****the number of lunar orbits in the solar year**and**the length of the eclipse year in 30-day months.**

all in lunar months. These triangles are to be constructed using the number series 11, 12, 13, 14 so as to form N:N+1 triangles (see figure 1).

Continue reading “Story of Three Similar Triangles”n.b. In the 1990s the primary geometry used to explore megalithic astronomy was N:N+1 triangles, where N could be non-integer, since the lunation triangle was just such whilst easily set out using the 12:13:5 Pythagorean triangle and forming the intermediate hypotenuse to the 3 point of the 5 side. In the 11:12 and 13:14 triangles, the short side is not equal to 5.

## Megalithic application of numeric time differences

Natural time periods between celestial phenomena
hold powerful insights into the numerical structure of time, insights which
enabled the megalith builders to access an explanation of the world unlike our
own. When looking at two similarly-long time-periods, the megalithic focussed
on the *difference* between them, these
causing the two periods to slide in and out of phase, generating a longer
period in which the two celestial bodies exhibit a complete ensemble of
variation, in their relationship to each other. This slippage of phase between
celestial periods holds a pattern purely based upon number, hidden from the
casual observer who does not study them in this way. Such numerical patterns
are only fully revealed through counting time and analysing the difference between
periods numerically.

For example, the solar year is
longer than the lunar year by 10 and 7/8 days (10.875 days) and three solar
years are longer than three lunar years by three times 10.875 days, that is by 32
and 5/8^{th} days (32.625 days), which is 32/29 of a single lunar month
of 29.53 days.

The earliest and only explicit evidence for such a three year count has been found at Le Manio’s Quadrilateral near Carnac (circa 4,000 BCE in Brittany, France) used the inches we still use to count days, a “day-inch” unit then widespread throughout later megalithic monuments and still our inch, 1/12 of the foot [Heath & Heath. 2011]. The solar-lunar difference found there over three years was 32.625 day-inches, is probably the origin of the unit we call the megalithic yard and the megalith builders appear to have adopted this differential length, between a day-inch count over three lunar and solar years, in building many later monuments.

Continue reading “Megalithic application of numeric time differences”