Sacred numbers within quantified geometries.

- Geometry 7: Geometrical Expansionabove: the dolmen of Pentre Ifan (wiki tab) In previous lessons, fixed lengths have been divided into any number of equal parts, to serve the notion of integer fractions in which the same length can then be reinterpreted as to its units or as a numerically different measurement. This allows all sorts of rescaling and … Continue reading “Geometry 7: Geometrical Expansion”
- Geometry 6: the Geometrical AMYBy 2016 it was already obvious that the lunar month (in days) and the PMY, AMY and yard (in inches) had peculiar relationships involving the ratio 32/29, shown above. This can now be explained as a manifestation of day-inch counting and the unusual numerical properties of the solar and lunar year, when seen using day-inch … Continue reading “Geometry 6: the Geometrical AMY”
- From Sacred Geometry: Language of the Angelsfrom Sacred Geometry: Language of the Angels, Appendix 1. (Available: first few weeks of 2021) This is relevant to many on-site posts. Metrology has appeared in modern times (phase five below) in reverse order, since humankind saw the recent appearance of many measures in different countries as indicative that past cultures made up units of … Continue reading “From Sacred Geometry: Language of the Angels”
- Geometry 4: Right Triangles within CirclesThis lesson is a necessary prequel to the next lesson. It is an initially strange fact that all the possible right triangles will fit within a half circle when the hypotenuse equals the half-circles diameter. The right angle will then exactly touch the circumference. From this we can see visually that the trigonometrical relationships, normally … Continue reading “Geometry 4: Right Triangles within Circles”
- Geometry 3: Making a circle from a counted lengthThe number of days in four years is a whole number of 1461 days if one approximates the solar year to 365¼ days. This number is found across the Le Manio Quadrilateral (point N to J) using a small counting unit, the “day-inch”, exactly the same length as the present day inch. It is an … Continue reading “Geometry 3: Making a circle from a counted length”
- Preface: The Metrology of the Brochsfeature picture: Broch of Mousa. The broch on the island of Mousa is the best-preserved of the many brochs in northern Scotland. It is thought to be some 2000 years old credit: Anne Burgess / Broch of Mousa / CC BY-SA 2.0 I wrote this preface for Euan MacKie who had resurrected his work on measures found within the brochs … Continue reading “Preface: The Metrology of the Brochs”
- Sacred Number and the Origins of CivilizationPublished by Inner Traditions Back Cover ANCIENT MYSTERIES / NEW SCIENCE “Richard Heath sweeps away the mechanistic and relativistic paradigm to reveal an earth-centered, celestial system founded upon the beauty of musical harmony and geometric symmetry.”–Robert Lawlor, author of Sacred Geometry and Voices of the First Day “Richard Heath effectively rewrites the book on the mysterious but accomplished … Continue reading “Sacred Number and the Origins of Civilization”
- Sacred Number and the Lords of TimeBack Cover ANCIENT MYSTERIES “Heath has done a superb job of collating his own work on the subject of megaliths with the objective views of many other researchers in the field. I therefore do not merely recommend reading this book but can state unequivocally it is a must read.”–John Neal, British metrologist and researcher and … Continue reading “Sacred Number and the Lords of Time”
- Sacred Geometry: Language of the AngelsExamining the angelic science of number, Richard Heath reveals how the development of human consciousness was no accident. The beauty and elegance we see in sacred geometry and in structures built according to those proportions are the language of the angels still speaking to us. Publisher Pages Description Reveals how the number science found in … Continue reading “Sacred Geometry: Language of the Angels”
- A Pyramidion for the Great Pyramidimage: By 1200 BC, the end of the Bronze Age, the Egyptian map of the world (above) showed nine bows or latitudes, numbers 4 to 9 including the Nile Delta, Delphi, Southern Britain and Iceland, a map based on an ancient geodetic survey. This post explores a pyramidion, now lost, which exceeded the apex height … Continue reading “A Pyramidion for the Great Pyramid”
- Recalibrating the Pyramid of GizaOnce the actual height (480 feet) and actual southern base length (756 feet) are multiplied, the length of the 11th degree of latitude (Ethiopia) emerges, in English feet, as 362880 feet. However, in the numeracy of the 3rd millennium BC, a regular number would be used. In the last post, it was noted that John … Continue reading “Recalibrating the Pyramid of Giza”
- Geometry 2: Maintaining integers using fractionsunderstanding the megalithic: circular structures: part 2 The megalithic sought integer lengths because they lacked the arithmetic of later millennia. So how did they deal with numbers? There is plenty of evidence in their early monuments that today’s inch and foot already existed and that these, and other units of measure, were used to count … Continue reading “Geometry 2: Maintaining integers using fractions”
- Geometry 1: πunderstanding the megalithic: circular structures: part 1 It would require 3 and a bit diameters to wrap around the circle – the ratio of 3 and a bit diameters to the perimeter is known as “Pi”, notated by the Greek symbol “π”. Half of the diameter, from the circle’s center to its edge, is named … Continue reading “Geometry 1: π”
- THE MEANING OF LE MENEC (PDF)This paper proposes that an unfamiliar type of circumpolar astronomy was practiced by the time Le Menec was built, around 4000 BCE. This observatory enabled the rotation of the earth and ecliptic location of eastern and western horizons to be known in real time, by observing stellar motion by night and solar motion by day. This method … Continue reading “THE MEANING OF LE MENEC (PDF)”
- A Brief Introduction to Ancient Metrology (2006)appended toSacred Number and the Origin of Civilisation There used to be an interest in metrology – the Ancient Science of Measures – especially when studying ancient monuments. However the information revealed from sites often became mixed with the religious ideas of the researcher leading to coding systems such as those of Pyramidology and Gematria. The general … Continue reading “A Brief Introduction to Ancient Metrology (2006)”
- Use of Ad-Quadratum at Angkor WatAd Quadratum is a convenient and profound technique in which continuous scaling of size can be given to square shapes, either from a centre or periphery. The differences in scale are multiples of the square root of two [sqrt(2)] between two types of square: cardinal (flat) and diamond (pointed).
- The Golden Mean compared to PIIn reviewing some ancient notes of mine, I came across an interesting comparison between the Golden Mean (Phi) and PI. They are more interesting in reverse: A phi square (area: 2.618, side: 1.618) has grown in area relative to a unit square by the amount (area: 0.618) plus the rectangle (area:1 ). This reveals the … Continue reading “The Golden Mean compared to PI”
- Use of foot ratios in Megalithic AstronomyThe ratios of ancient metrology emerged from the Megalithic innovations of count&compare: counting time as length and comparing lengths as the longest sides of right triangles. To compare two lengths in this way, one can take a longer rope length and lay it out (say East-West), starting at the beginning of the shorter rope length, … Continue reading “Use of foot ratios in Megalithic Astronomy”
- Old Yard’s Mastery of the Square Root of 2The old yard was almost identical to the yard of three feet, but just one hundredth part smaller at 2.87 feet. This gives its foot value as 99/100 feet, a value belonging to a module very close to the English/Greek which defines one relative to the rational ratios of the Historical modules. So why was … Continue reading “Old Yard’s Mastery of the Square Root of 2”
- Models of Time within Henges and Circlesimage: composite, see figure 1 below Presenting important information clearly often requires the context be shown, within a greater whole. Map makers often provide an inset, showing a larger map at a smaller scaling (as below, of South America) within a detailed map (of Southern Mexico). Megalithic astronomy generated maps of time periods, using lines, … Continue reading “Models of Time within Henges and Circles”
- Palsson’s Sacred Image in IcelandExtracted from The Structure of Metrology, its Classification and Application (2006) by John Neal and notes by Richard Heath for Bibal Group, a member of which, Petur Halldorsson, has taken this idea further with more similar patterns on the landscape, in Europe and beyond. Petur thinks Palsson’s enthusiasm for Pythagorean ideas competed with what was … Continue reading “Palsson’s Sacred Image in Iceland”
- Megalithic Measurement of Jupiter’s Synodic Periodimage: Jupiter with now-shrunken red spot – Hubble Space Telescope 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, … Continue reading “Megalithic Measurement of Jupiter’s Synodic Period”
- Story of Three Similar Trianglesfirst 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 … Continue reading “Story of Three Similar Triangles”
- Megalithic application of numeric time differencesNatural 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 … Continue reading “Megalithic application of numeric time differences”