Post by glaucus on Mar 20, 2022 19:15:29 GMT
The number π (/paɪ/; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159. It is defined in Euclidean geometry as the ratio of a circle's circumference to its diameter, and also has various equivalent definitions. It appears in many formulas in all areas of mathematics and physics. The earliest known use of the Greek letter π to represent the ratio of a circle's circumference to its diameter was by the Welsh mathematician William Jones in 1706. It is also referred to as Archimedes's constant.
As an irrational number, π cannot be expressed as a common fraction, although fractions such as 22/7 are commonly used to approximate it. Equivalently, its decimal representation never ends and never settles into a permanently repeating pattern. Its decimal (or other base) digits appear to be randomly distributed, and are conjectured to satisfy a specific kind of statistical randomness.
It is known that π is a transcendental number: It is not the root of any polynomial with rational coefficients. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge.
Philip Sedgwick discusses Pi aspect in his book The Astrology of Transcendence:
The Astrology of Transcendence
page 186 to 187
"It was speculated that by dividing the 360 degree circle by the mathematical pi (3.416) the 105 degree would be derived. Actual calculations showed that the 105 degrees result from dividing the wheel by 3.4286, hardly pi or any mathematical significance, for that matter. Still, pi was intriguing. Division of 360° by 3.1416 resulted in an arc of 114.5913°. Actually, this is rather close to an angle of 115°. Converting the decimal equivalent of the quotient to minutes and seconds yields 114°35'28.65".
Pi is an integral part of the circle's circumference to the diameter. The ancient Greeks also used pi mathematically to represent peripherion which literally applied means "periphery". The concepts associated with the nearly 115 degree aspect relates a ratio of the circumventing events in the life (circumference) to the internal structures of the native (diameter). As a result, this provides the quality of the perception of the experiences about the native as it gives those not directly relating to the native a picture of what they seem to be. This reception given to others may not be exactly the essence of the native, as typified by the more than 3 to 1 ratio. "
"Both the 105 and 115 (circa) degree relationships bear one quality in common. They both provide to the entity involved the nature or process of crystalization. Both represent structure, structure which forms its basis in solid foundation and clear, precise Universal thinking. In this exists the potentiality to to with the course of the Universe which leads to the ultimate clarity of form; it occurs when Thy Will Be Done. Both these aspects internally project the need of transcendence of the self. The transcendence optimally occurs when the native rises above the self to be integrated with the totality of the thinking of mankind. That is, the native realizes that the input one holds is as valid as anyone else's based upon the revelation that one's existential foundation has been as real anyone else's. They now become contributable. They are now part of the crystal's reflected array of color, light and life."
What he wrote made me sit up straight because I happen to have Moon and Mercury in a 105° aspect with an orb of only 10 minutes. I have Transneptunian dwarf planet candidate cubewano (Classical Kuiper Belt Object) Varuna in a 24th Harmonic Triangle with that aspect with Varuna square Moon with an orb of 9 minutes and in 165° aspect with Mercury with an orb of 19 minutes. The proportionate orb for the 24th harmonic aspects based on 15 degree orb for conjunction is 37 minutes, 30 seconds. At the least, my emotional nature and mental processes involve evolutionary intensification. Varuna was named after the Vedic God of the Oceans, and he is the deity of the nakshatra Satabisha which is where my Moon in Sidereal Aquarius is located at.
Zane Stein's site:
Squine (105 degrees): Charles Jayne studied this aspect, which I have not found a symbol for. He said it was like a hybrid between a square and a trine. You've got some of the laziness and ease that comes with a trine, but at the same time some of the problems of the square. You've got an incomplete tool that doesn't have quite a sharp enough edge but it isn't fully automatic, so you have to put some energy into it, and this is essential to do a good job. I call it the "Diamond in the rough aspect". 1 degree orb even with Sun or Moon.
Johndro (165 degrees) Some people also call this the Quindecile. Where you have this aspect, you have a dogged determination. You don't know when to quit, won't quit...even if the proposition is found to be unfeasible, you can't let go, can't stop. It is an aspect of unrelenting motivation, obsession, and determination, and can even cause separation. 1 degree orb even with Sun or Moon.
Not every astrologer agrees with Noel Tyl referring to the 165° aspect as the Quindecile which is really the 24° degree aspect. It is the 1/15th harmonic aspect. Quindecile is referring to the 15th Harmonic. Quindecile is not referring to 15° divisions. It would be like claiming that Septile is referring to 7° divisions and not the 7th Harmonic. Robert Blasckhe even referred to the 165° aspect as the Contraquindecile in his book Sabian Aspect Orbs.
I investigated the angle based on Pi
360° divided by 3.14159 = 114.5916558175955°
114°35'29'' is Pi's angle
Looking for a recent exact Moon-Uranus Pi transit in Solar Fire,
I found an exact Moon-Uranus Pi Aspect on March 16th, 2022 at 10:28:27 AM here in Tacoma, Washington
According to Sirius astrology program's harmonic grid,
Pi Aspect has the following corresponding Harmonic Aspects with orb (deviation from being exact)
113/355 - 0 min (with strength of 100%)
106/333 - 0 min (with strength of 93%)
99/311 - 0 min (with strength of 86%)
The Pi Aspect seems to be the 113/355 Aspect.
The Pi Aspect has the following corresponding Harmonic Aspects with the orb of the conjunction in the particular harmonic:
113/355 - 1 min
106/333 - 1 deg 2 min
99/311 - 2 deg 3 min
I am quite amazed that the 355th Harmonic conjunction is almost exact. I haven't seen that with the other micro-aspects that I investigated.
The proportionate orb for the harmonic aspects based on 15 degree orb for conjunction:
355th - 1 min 32 sec
333rd - 2 min 42 sec
311th - 2 min 53 sec