This is a personal project that I am working on to help me to understand and apply discrete math. It is foundationally based on the module 3 critical thinking project and goes down a much larger rabbit hole from there. These are my notes.

I am attempting to use my understanding of the orbit of Venus to correlate mathematical principles such as the golden ratio, the Fibonacci sequence, and to understand how recursive definitions are used in the comparison. I am also seeking to improve on my closed formulas. I do not completely understand how to write them.

Is this a correct statement?

• The synodic cycle of Venus around the earth is a geometric sequence.This can also be defined as a sequence in which the ratio between the element and the proceeding element continues to be constant is a geometric sequence.

Note * The 5-pointed star pattern formed by the Venus synodal cycle around the earth is referenced in astrology and sacred geometry as the Venus Rose.

Is this a correct statement?

• The geometric sequence in the rose of Venus synodal cycle around the earth is infinite (13,8,5,13,8,5,13,8,5,...)

Is this a true statement?

• This is not a recursive sequence because it doesn't create a spiral cycle, however the degree of movement of the nodes of Venus 1 degree every 113.33 years does. How do I express this in a formula? That is to say, how do I write the recursive definition of this?

• If I am wrong about this and it is in fact a recursive sequence, then what is the recurrence equation?
• To clarify.... How would I express the recursive definition of the sequence (13,8,5,13,8,5,...)?
• How would I write the recursive definition of the sequence (113.33,1,113.33,1,...)
• Am I understanding sequences correctly in the above? I understand the definition of a sequence as a list of numbers in a specified order. Thus, the synodal geometric sequence of the orbit of Venus around the earth is either (13,8,5,13,8,5,...) or it is (8,5,8,5,...)
• Is this statement correct - The sequence of the degree of movement of the 5 nodes of Venus is (113.33,1,113.3,1,...)?
• I am under the impression there is no recursive definition because there in no smaller index it is simply a closed formula of 13-8=5 repeated

The venus synodic cycle around the earth is a geometric sequence. (584 days Venus year/365 days Earth year) = 1.6 years 5 Venus synodic cycles in 8 years 5 /8 = 1.6 13 Venus revolutions in 8 earth years 13/8= 1.6

This "golden" number, 1.618 is represented, as are the repeated Fibonacci sequence numbers 5,8,13.

Is this a true statement?

• The repeated golden spiral that is created in the Venus rose is a visual illustration of this sequence (13,8,5,13,8,5,13,8,5.....)

There full orbit of Venus around the earth is 5 cycles of 8 years each = 40 years. Each node in the pentagram of the Venus orbit is a new cycle of the 5 that creates a new golden spiral.

The ratio of 8:5 is phi (1.618...). This is the golden proportion and is found in the Fibonacci numbers. 8 Earth years = 5 synodic Venus cycles. 1.6 x 5 = 8

This sequence can be related to the Fibonacci numbers and common sequence Fn = Fn-1+Fn-2 with F1=F2=1 but

• ??? I am unsure how to write the formula. Specifically, the conjunctive movements.

Because the degrees of each of these conjunctions also progressively move forward in the zodiac, we see the nature of a larger time cycle within the nodes Venus's movement. This list denotes the progression of the conjunctions. YEAR SN Conjuncts NN NN Conjuncts SN ---------------------------------------------------------------------------- -500 May 17th @ 24 Taurus November 16th @ 24 Scorpio -400 May 17th @ 25 Taurus November 16th @ 25 Scorpio -300 May 18th @ 26 Taurus November 17th @ 26 Scorpio -200 May 19th @ 27 Taurus November 18th @ 27 Scorpio -100 May 20th @ 27 Taurus November 20th @ 27 Scorpio 0 May 20th @ 28 Taurus November 20th @ 28 Scorpio 100 May 22nd @ 29 Taurus November 21st @ 29 Scorpio 200 May 23rd @ 0 Gemini November 22nd @ 0 Sag 300 May 24th @ 1 Gemini November 23rd @ 1 Sag 400 May 24th @ 2 Gemini November 23rd @ 2 Sag 500 May 25th @ 3 Gemini November 24th @ 3 Sag 600 May 26th @ 4 Gemini November 27th @ 4 Sag 700 May 27th @ 4 Gemini November 27th @ 4 Sag 800 May 27th @ 5 Gemini November 27th @ 5 Sag 900 May 28th @ 6 Gemini November 28th @ 6 Sag 1000 May 30th @ 7 Gemini November 29th @ 7 Sag 1100 May 31st @ 8 Gemini December 1st @ 8 Sag 1200 May 31st @ 9 Gemini December 1st @ 9 Sag 1300 June 1st @ 10 Gemini December 2nd @ 10 Sag 1400 June 2nd @ 11 Gemini December 3rd @ 11 Sag 1500 June 3rd @ 12 Gemini December 4th @ 12 Sag 1600 June 3rd @ 13 Gemini December 4th @ 13 Sag 1700 June 5th @ 14 Gemini December 7th @ 14 Sag 1800 June 5th @ 14 Gemini December 7th @ 14 Sag 1900 June 7th @ 15 Gemini December 8th @ 15 Sag 2000 June 7th @ 16 Gemini December 8th @ 16 Sag 2100 June 8th @ 17 Gemini December 9th @ 17 Sag 2200 June 9th @ 18 Gemini December 10th @ 18 Sag 2300 June 10th @ 19 Gemini December 11th @ 19 Sag 2400 not available from true - node The above covers 2,800 years of movement of Venus's nodal conjunctions The first line is conjunctions at 24 Taurus and 24 Scorpio in 500 BC The last line is conjunctions at 19 Gemini and 19 Sag in 2300 AD Note also, these nodal conjunctions occur at the time the Sun is conjunct the same point. The movement of the nodal conjunctions of Venus in this time period is 113.33 years per degree of forward movement. In my understanding, this means that the 5 nodes created by the 8 cycles of Venus in 13 years shift forward 1 degree every 113.33 years. Which creates an infinite sequence of a repeating golden spiral ratio. Thus, creating the famous synodal rose of Venus.

My questions simplified

• Is the sequence (13,8,5,13,8,5,...) Correct in describing the orbit of Venus around the earth?
• How would I write the Recursive definition of the above sequence if it is correct?

f(0)= 5

f(n) = f+3

???

• However, if it is not a recursive sequence as I postulated above then there is no recursive definition. Is this correct?

• the Closed formula would be the Fibonacci numbers is this correct?
• If this is correct, how would I write this in formula?