Triangle, Square, and Hexagon │ Basic Figures Filling the Space

The Equiangular Period Spiral includes periods, distances and velocities. It is delimited by three basic equiangular figures – the triangle, the square (more correctly the rectangle) and the hexagon. Nicolas d'Oresme wrote in his major work Le Livre du Ciel et du Monde (The Book of the Heaven and the Earth, 1377):

» Notwithstanding that He is everywhere, still is He absolutely indivisible and the same time infinite with respect to the three qualities that are divisible in living creatures, which we call duration, position, and power or perfection; for temporal duration of creatures is divisible in succession; their position, especially of material bodies, is divisible in extension; and their power is divisible in any degree or intensity […] Besides the varieties of trinity noted there, there is another which is pertinent to our present discussion, because, in accord with what we said […], there are three regular plane figures – the triangle, the square, and the hexagon – each of which we can imagine to be capable of filling so completely a flat area or surface that it is absolutely impossible that there could be more space to be filled; likewise there are three divine persons, each of whom fills all space. Isaiah the Prophet spoke of them thus: Holy, Holy, Holy, Lord God, etc. all the earth is full of thy glory. And there is one God, who spoke through His Prophet Jeremiah: I will fill the heaven and earth; and of whom Virgil said: All things are replete with Jove. « (Book IV, Chapter 10).

A page from d'Oresme's Livre du Ciel et du Monde, showing the celestial spheres:
Although the order of the spheres is conventional, with the Moon and Mercury
closest the Earth and Saturn and the stars farthest, the spheres are convex upward
centered on God rather than convex downward centered on the Earth.
[Paris, Bibliothèque Nationale de France, Manuscrits, Fr. 565, fo 69].

The Harmony of Being | Geometry in Man, Nature, and Cosmos

Proportional roots: (a) the √2 proportion, (b) the √3 proportion,
and (c) the golden mean (Phi) proportion.

Loai M. Dabbour (2012) - Geometry describes the assertions of a mathematical order of the intrinsic nature of the universe. Geometry is the very basis of our reality, and we live in a coherent world governed by underlying laws. Johannes Kepler stated that geometry is underpinning the cosmos, which was based on Plato’s ideas that God created the universe according to a geometric plan. The structure of the universe is determined by and revealed as certain mathematical and geometric constants which represent a confirmation that proportions are the underlying fabric of nature. This can be seen in man, nature, and cosmos.

Root proportions based on the square.

By contemplating geometric proportions, an understanding towards the sacred truth can be obtained since geometric proportions are one of the definitive geometric qualities of life itself. The Holy Quran tells us that man has within himself all what is reflected in the universe - the best proportions. Man is the core of God’s creatures; he possesses the most harmonious proportions, reflecting of the Divine harmony of being. "We have indeed created man in best of forms" – proportions (Surah At-Tin, 95:4). Leonardo da Vinci illustrated the mathematical proportions of the human body, showing that human being exhibits clearly golden mean proportions in his body based on ratios of 1.618.The Vitruvian Man drawn by Leonardo Da Vinci is based on Vitruvius, who believed that if human proportions could be incorporated into buildings, they would become perfect in their geometry. According to Vitruvius, the distance from fingertip to fingertip should be the same as that from head to toe. The sacred mean rules can be seen in the ratios of body parts throughout the human body. The human body contains in its proportions all the important geometric geodesic measures and functions. The proportions of ideal man are at the center of a circle of invariant cosmic relationships.

Proportions of Venus’ and Earth’s mean orbits.

The mathematical harmony of the universe can be seen from the proportions of the planets in our solar system. For example, the ratio of the sacred mean can be seen in the rotations of Venus and Earth around the Sun in that for each five years that the Earth rotates around the Sun, Venus rotates around it eight times. The connection between 5 and 8, both of which are Fibonacci numbers, is the golden mean proportion (8/5 = 1.6). The result of this motion is that Venus draws a pentagon around the Sun every eight years (Figure A). Figure B shows that a circle is drawn, which represents Venus’ mean orbit. A pentagon is constructed inside it and a small circle placed through the arm-crossing points. The radius of this small circle divides the radius of the large one into golden sections and can be used to space Venus’ orbit from Earth’s orbit. It can be seen from the agreement between eightfold and fivefold geometries that eight touching circles are drawn from Venus’ mean orbit. In turn, the circumference circle is enclosing these eight circles, defining Earth’s mean orbit. The ratio of the mean orbits of Venus’s to Earth is the √2 proportion. The geometric representation of these orbits creates the golden mean proportion.

The Measure of the Circle | Math for Mystics

Pi (π) is the ratio of the circumference of a circle to its diameter. 
As a fraction, its closest approximations are 22/7, 333/106 and 355/113.

Projection on the plane of the ecliptic of the parabolic
orbits of 72 comets, 1802. Engraving by Wilson Lowry after
Johann Elert Bode.

Circle of Fifths, and relationship of relative
minor keys to major key signatures.

 

"The circle is one of the noblest representations of Deity, in his noble works of human nature. It bounds, determines, governs, and dictates space, bounds latitude and longitude, refers to the Sun, Moon, and all the planets, in direction, brings to the mind thoughts of eternity, and concentrates the mind to imagine for itself the distance and space it comprehends. It rectifies all boundaries; it is the key to information of the knowledge of God; it points to each and every part of God's noble work."

John Davis (1845): The Measure of the Circle [p. 12].

Math for Mystics | # 1

The Pythagorean Definition of God

St. Bernard of Clairvaux: "God is breadth and length, height and depth."

US Stocks May Double into 2017 | Martin Armstrong

HERE
This is in line with the Lunar Node Projection for the US-Economy:
HERE & HERE 

Martin Armstrong (06/18/2015) - 18,500 [in the DJIA] has capped the US stock market for right now, so we're not breaking out. We'll get through that. The next level is 23,000 [after a consolidation in fall 2015]. If we get through that area ... then you're looking at the final phase transition that will probably take us into 2017 where, yes, the stock market can double.

[...] With bond yields pushed down to all-time lows, bond prices are now at all-time highs. As rates eventually start to move up, large investors will try to prevent losses by shifting into other areas with US assets, particularly stocks and real estate, serving as the most likely destination.