#### numeracy through Geometry and astronomy

Below are lessons in what are thought to have been megalithic methods, that involved measures, geometrical procedures and astronomical techniques.

- Astronomy 3: Understanding Time Cyclesabove: a 21-petal object in the Heraklion Museum which could represent the 21 seven-day weeks in the 399 days of the Jupiter synod. [2004, Richard Heath] One of the unfortunate aspects of adopting the number 360 for calibrating the Ecliptic in degrees is that the megalithic counted time in days and instead saw the ecliptic … Continue reading “Astronomy 3: Understanding Time Cycles”
- 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”
- Astronomy 2: The Chariot with One WheelWhat really happens when Earth turns? The rotation of Earth describes periods that are measured in days. The solar year is 365.242 days long, the lunation period 29.53 days long, and so forth. Extracted from Matrix of Creation, page 42. Earth orbits the Sun and, from Earth, the Sun appears to move through the stars. … Continue reading “Astronomy 2: The Chariot with One Wheel”
- Astronomy 1: Knowing North and the Circumpolar Skyabout how the cardinal directions of north, south, east and west were determined, from Sacred Number and the Lords of Time, chapter 4, pages 84-86. Away from the tropics there is always a circle of the sky whose circumpolar stars never set and that can be used for observational astronomy. As latitude increases the pole … Continue reading “Astronomy 1: Knowing North and the Circumpolar Sky”
- Geometry 5: Easy application of numerical ratiosabove: Le Manio Quadrilateral The last lesson showed how right triangles are at home within circles, having a diameter equal to their longest side whereupon their right angle sits upon the circumference. The two shorter sides sit upon either end of the diameter (Fig. 1a). Another approach (Fig. 1b) is to make the next longest … Continue reading “Geometry 5: Easy application of numerical ratios”
- 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”
- 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”