Showing posts with label Earth. Show all posts
Showing posts with label Earth. Show all posts

Sunday, March 25, 2018

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].

Thursday, March 2, 2017

Friday, February 17, 2017

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.

Saturday, January 7, 2017

Harmony of the Spheres | Dance of the Planets


James Ferguson’s (1710-1776) representation of the apparent motion of the Sun, Mercury, and Venus from the Earth, based on similar diagrams by Giovanni Cassini (1625-1712) and  Roger Long (1680-1770). Taken from the "Astronomy" article in the first edition of the Encyclopædia Britannica (1771; Volume 1, Fig. 2 of Plate XL facing page 449). This geocentric diagram shows, from the location of the Earth, the Sun's apparent annual orbit, the orbit of Mercury for 7 years, and the orbit of Venus for 8 years, after which Venus returns to almost the same apparent position in relation to the Earth and Sun. In Arabic, Venus is called “El Zahra” - the flower. See HERE + HERE + HERE + HERE

Earth - Mercury Cycle.
This and all following graphics by John Martineau.
Earth - Venus Cycle:
Earth = 8 years x 365.256 days/year = 2,922.05 days
Venus = 13 years x 224.701 days/year = 2,921.11 days (ie. 99.9%)
Earth - Mars Cycle.
Earth - Jupiter Cycle.
Saturn - Uranus Cycle.
Jupiter - Saturn Cycle.
Venus - Mars Cycle.
The radius of the Moon compared to the Earth's is 3:11
Radius of Moon = 1,080 miles = 3 x 360
Radius of Earth = 3,960 miles = 11 x 360 = 33 x 1 x 2 x 3 x 4 x 5
Radius of Earth plus Radius of Moon = 5,040 miles = 1 x 2 x 3 x 4 x 5 x 6 x 7 = 7 x 8 x 9 x 10

The ratio 3:11 is 27.3%, and the orbit of the Moon takes 27.3 days, which is also the average rotation period of a sunspot. The closest to farthest distance ratio that Venus and Mars each experiences in the Mars-Venus dance is also 3:11. The Earth orbits between them. The sizes of the Moon and the Earth is drawn to scale in the last illustration above, where the perimeters of the dotted square and the dotted circle are of the same length: The perimeter of the dotted red square is 4 x Earth’s diameter = 4 x 7,920 miles = 31,680 miles. The circumference of the dotted blue circle is 2 pi x radius = 2 x 3.142 x 5040 miles = 31,667 miles (ie. 99.9%).

Saturday, September 19, 2015

Squaring the Circle with the Earth and the Moon

The perimeter of a square around the Earth equals the perimeter of a
circle drawn through the center of the Moon.
Credits: Michæl Paukner
Common Wisdom (2015) - Squaring the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge. More abstractly and more precisely, it may be taken to ask whether specified axioms of Euclidean geometry concerning the existence of lines and circles entail the existence of such a square.

In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem which proves that pi (π) is a transcendental, rather than an algebraic irrational number; that is, it is not the root of any polynomial with rational coefficients. It had been known for some decades before then that the construction would be impossible if pi were transcendental, but pi was not proven transcendental until 1882. Approximate squaring to any given non-perfect accuracy, in contrast, is possible in a finite number of steps, since there are rational numbers arbitrarily close to π.

Tuesday, September 11, 2012

SPX vs Alignments & Oppositions of Mercury-Venus-Jupiter-Earth
























EAR and/or MER and/or VEN and/or JUP = 0°or 180° to EAR and/or MER and/or VEN and/or JUP [HELIO - MAXORB 1°]

07.29.2012 - 07.30.2012
08.12.2012 - 08.13.2012
09.10.2012 - 09.11.2012
09.20.2012 - 09.21.2012

10.04.2012 - 10.05.2012
10.21.2012 - 10.22.2012
11.18.2012 - 11.19.2012
11.20.2012 - 11.21.2012
12.03.2012 - 12.04.2012
12.18.2012 - 12.19.2012
01.03.2013 - 01.04.2013
01.16.2013 - 01.17.2013
01.18.2013 - 01.19.2013
02.17.2013 - 02.18.2013
02.28.2013 - 03.01.2013
03.04.2013 - 03.05.2013
03.28.2013 - 03.30.2013
04.04.2013 - 04.05.2013
05.12.2013 - 05.13.2013
05.16.2013 - 05.19.2013
06.19.2013 - 06.21.2013
07.03.2013 - 07.04.2013
07.10.2013 - 07.11.2013
08.05.2013 - 08.06.2013
08.25.2013 - 08.26.2013
09.11.2013 - 09.12.2013
10.02.2013 - 10.03.2013
10.20.2013 - 10.21.2013
11.02.2013 - 11.03.2013
12.22.2013 - 12.23.2013
12.29.2013 - 12.30.2013
 


Calculated and charted with Sergey Tarassov's Timing Solution.

Wednesday, March 28, 2012

SPX vs EAR - MAR Cycle

23.09.2011  06:18 FR = EAR 0 MAR [H40]
11.10.2011  07:36 TU = EAR 0 MAR [H40]

28.10.2011  14:55 FR = EAR 0 MAR [H40]
14.11.2011  06:49 MO = EAR 0 MAR [H40]
30.11.2011  12:17 WD = EAR 0 MAR [H40]
16.12.2011  09:51 FR = EAR 0 MAR [H40]
01.01.2012  01:45 SU = EAR 0 MAR [H40]
16.01.2012  15:15 MO = EAR 0 MAR [H40]
01.02.2012  04:11 WD = EAR 0 MAR [H40]
16.02.2012  19:30 TH = EAR 0 MAR [H40]
03.03.2012  14:50 SA = EAR 0 MAR [H40]
19.03.2012  17:46 MO = EAR 9 MAR [H40]
05.04.2012  03:48 TH = EAR 18 MAR [H40]

21.04.2012  23:57 SA = EAR 27 MAR [H40]
09.05.2012  07:38 WD = EAR 36 MAR [H40]
27.05.2012  03:51 SU = EAR 45 MAR [H40]
14.06.2012  13:52 TH = EAR 0 MAR [H40]
03.07.2012  13:34 TU = EAR 0 MAR [H40]
23.07.2012  03:07 MO = EAR 0 MAR [H40]
12.08.2012  06:14 SU = EAR 0 MAR [H40]
01.09.2012  21:39 SA = EAR 0 MAR [H40]
23.09.2012  00:34 SU = EAR 0 MAR [H40]
14.10.2012  14:23 SU = EAR 0 MAR [H40]
05.11.2012  13:15 MO = EAR 0 MAR [H40]
27.11.2012  22:48 TU = EAR 0 MAR [H40]
20.12.2012  18:13 TH = EAR 0 MAR [H40]
12.01.2013  23:28 SA = EAR 0 MAR [H40]
05.02.2013  13:11 TU = EAR 0 MAR [H40]
01.03.2013  08:22 FR = EAR 0 MAR [H40]
25.03.2013  05:25 MO = EAR 0 MAR [H40]
17.04.2013  20:38 WD = EAR 0 MAR [H40]
11.05.2013  01:07 SA = EAR 0 MAR [H40]
02.06.2013  13:43 SU = EAR 0 MAR [H40]
24.06.2013  06:48 MO = EAR 0 MAR [H40]