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.
- The Stonehenge Crop Circle of 2002
One sees most clearly how a single concrete measure such as 58 feet can take the meaning of the design into the numbers required to create it. However, metrology of feet and types of feet can hide the elegance of a design. - St Peter’s Basilica: A Golden Rectangle Extension to a Square
HAPPY NEW YEAR above: The Basilica plan at some stage gained a front extension using a golden rectangle. below: Later Plan for St. Peter’s 16th–17th century. Anonymous. Metropolitan Museum. The question is whether the extension from a square was related the previous square design. The original square seems quite reworked but similar still to the … Continue reading “St Peter’s Basilica: A Golden Rectangle Extension to a Square” - Double Square and the Golden Rectangle
above: Dan Palmateer wrote of this, “it just hit me that the conjunction of the circle to the golden rectangle existed.” Here we will continue in the mode of a lesson in Geometry where what is grasped intuitively has to have reason for it to be true. It occurred to me that the square in … Continue reading “Double Square and the Golden Rectangle” - Working with Prime Numbers
Wikipedia diagram by David Eppstein : This is an updated text from 2002, called “Finding the Perfect Ruler” Any number with limited “significant digits” can be and should be expressed as a product of positive and negative powers of the prime numbers that make it up. For example, 23.413 and 234130 can both be expressed as … Continue reading “Working with Prime Numbers” - Vectors in Prehistory 2
In early education of applied mathematics, there was a simple introduction to vector addition: It was observed that a distance and direction travelled followed by another (different) distance and direction, shown as a diagram as if on a map, as directly connected, revealed a different distance “as the crow would fly” and the direction from … Continue reading “Vectors in Prehistory 2” - The Fourfold Nature of Sun and Moon
A previous post explained the anatomy of the primary celestial cycles of the Sun and Moon. The “resting” part of these cycles are the winter solstice (opposite the summer solstice which was today) and the dark moon (which is coming in a week, after the waning half moon day before yesterday). In the resting phase, … Continue reading “The Fourfold Nature of Sun and Moon” - Astronomy 3: Understanding Time Cycles
above: 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 Expansion
above: 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 AMY
By 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 Wheel
What 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 Sky
about 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 ratios
above: 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 Circles
This 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 length
The 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 fractions
understanding 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”