By Robert Lawlor
An advent to the geometry which, as glossy technological know-how now confirms, underlies the constitution of the universe.
The thinkers of historical Egypt, Greece and India well-known that numbers ruled a lot of what they observed of their global and consequently supplied an method of its divine writer. Robert Lawlor units out the approach that determines the measurement and the shape of either man-made and normal buildings, from Gothic cathedrals to plant life, from track to the human physique. by way of additionally concerning the reader in sensible experiments, he leads comfortably from uncomplicated ideas to a snatch of the logarithmic spiral, the Golden percentage, the squaring of the circle and different ubiquitous ratios and proportions.
Art and Imagination: those large-format, gloriously-illustrated paperbacks conceal jap and Western faith and philosophy, together with fantasy and magic, alchemy and astrology. the celebrated authors convey a wealth of information, visionary pondering and obtainable writing to every exciting topic. 202 illustrations and diagrams, fifty six in colors.
This is 2002 Reprint.
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Extra resources for Sacred Geometry: Philosophy & Practice (Art and Imagination)
To illustrate the proportion A : B:: E: F or 16:24::12:18= 213 draw line segment E = 12 and line A = 16 on the same horizontal with ends tangent a t 0. Raise a perpendicular B from the end of line A to establish any desired proportional relationship to 16, in this case, B = 24. The ratio A : B = 213. This diagonal will always intersect with a perpendicular dropped from the end of E so that line segment F will be in relation to E in the same ratio as B is to A, thus geometrically verifying that when one has three terms of a four-term proportion it is always possible to find the fourth term.
2. ,/2 function. From the given unity square with A as centre and AA as radius, swing an arc cutting the X axis at B. With Y as centre and radius YB, swing a semicircle cutting the Y axis at B'. With B as centre and radius BB swing an arc cutting the X axis at point C (5 units). With Y as centre and radius YC swing a semicircle cutting the Y axis at C' to determine square 3 and its germ along the X axis. Repeat to draw squares 4 , 5 . . The root of square 1 becomes the germ of 2; the root of square 2 becomes the germ of 5; the root of square 5 becomes the germ of 12.
Historically this unique geometric proportion of two terms has been given the name 'Golden Proportion', and is designated by the 21st letter of the Greek alphabet, phi (4), although it was known by cultures much older than the Greek. There are two importantly different ways to consider this primary geometric proportion in relation to Unity. The first occurs when the largest term (in this case (a+ b) is greater than 1 or unity. The second case occurs when the largest term (a+ b) equals unity or 1 (in formula a: b : : b :1).
Sacred Geometry: Philosophy & Practice (Art and Imagination) by Robert Lawlor