# Fibonacci sequence

brunardot
Fibonacci sequence and circles

The Fibonacci sequence is a portion of the "revised" Fibonacci sequence.

Five terms of the revised Fibonacci sequence can be found within five different structural parts of a circle.

What are the structural parts of said circle?

Last edited:

Jimmy Snyder
brunardot said:
The Fibonacci sequence is a portion of the "revised" Fibonacci sequence.
What is the revised Fibonacci sequence?

brunardot
Revised Fibonacci sequence

jimmysnyder said:
What is the revised Fibonacci sequence?

Thanks for asking a direct question. I'm used to questions regarding my intelligence rather than questions regarding my statements.

The revised Fibonacci sequence is the first unending Natural integer sequence of the unending, simple additive, sequences of the Brunardot Series, which series is ubiquitous throughout all phenomena:

x, x^2 - 1, x^2, 2x^2 - 1, 3x^2 - 1...

With the above, Brunardot Series, the answer to the initial question should be evident.

Last edited:
I still don't understand this "revised" sequence... Could you please explane it a bit?

brunardot
1, 0, 1, 1, 2...

xJuggleboy said:
I still don't understand this "revised" sequence... Could you please explane it a bit?

Brunardot said:
Thanks for asking a direct question. I'm used to questions regarding my intelligence rather than questions regarding my statements.

The revised Fibonacci sequence is the first unending Natural integer sequence of the unending, simple additive, sequences of the Brunardot Series, which series is ubiquitous throughout all phenomena:

x, x^2 - 1, x^2, 2x^2 - 1, 3x^2 - 1...

With the above, Brunardot Series, the answer to the initial question should be evident.

The revised Fibonacci sequence (one or two additional terms, depending upon your definition of FS, at the beginning) is the first unending Natural integer (x equals One, "1") sequence of the unending, simple additive, sequences of the Brunardot Series, which series is ubiquitous throughout all phenomena:

x, x^2 - 1, x^2, 2x^2 - 1, 3x^2 - 1...

(Thus, 1, 0, 1, 1, 2... The first term is the revision; so as to, correlate with Nature. This would also pin the unrevised FS as beginning with 0, 1 and not 1, 1)

With the above, Brunardot Series, the answer to the initial question should be evident. (Hint: Consider the circle as a special ellipse.)

Last edited:
Jimmy Snyder
brunardot said:
1, 0, 1, 1, 2

0 - the focal length *
1 - the major axis *
1 - the minor axis *
2 - the diameter

where * means "Treating the circle as a special case of an ellipse"

brunardot
Not quite correct

jimmysnyder said:
0 - the focal length *
1 - the major axis *
1 - the minor axis *
2 - the diameter

where * means "Treating the circle as a special case of an ellipse"

No; though you've got the idea. Your answer is contrived, in mixed terms, to fit the sequence.

I don't see how the major axis and the diameter can have different values?

The answer is best in elliptical terms, such that each term represents a different elliptical, structural part, that applies to all ellipses (the parts, not the values) as well as the special ellipse.

Not sure if I've helped or confused?

Last edited:
Jimmy Snyder
brunardot said:
The answer is best in elliptical terms, such that each term represents a different elliptical, structural part, that applies to all ellipses (the parts, not the values) as well as the special ellipse.
Oops, my education did not include definitions of the structural parts of an ellipse. Here is what I should have written:

0 - the distance between the two foci *
1 - the distance from the center to the ellipse along the minor axis *
1 - the distance from the center to the ellipse along the major axis *
2 - the diameter

where * means "Treating the circle as a special case of an ellipse"

Note that I switched 'minor' and 'major' from what I had originally posted.

You can translate this into the proper structural parts.

brunardot
Solution accepted

jimmysnyder said:
Oops, my education did not include definitions of the structural parts of an ellipse. Here is what I should have written:

0 - the distance between the two foci *
1 - the distance from the center to the ellipse along the minor axis *
1 - the distance from the center to the ellipse along the major axis *
2 - the diameter

where * means "Treating the circle as a special case of an ellipse"

Note that I switched 'minor' and 'major' from what I had originally posted.

You can translate this into the proper structural parts.

I'll accept your solution, as my given statements are difficult to construe.

I would prefer:

1 = perigee
0 = soliton (half a wave or half the focal length)
1 = vector (line from a focus to the end of the minor diameter)
1 = apogee
2 = major diameter.

You succeeded because you first asked a pertinent question that most assume as irrelevant.

Few persons are educated in the structural parts of an ellipse. Do you realize that every elliptical shape has all its structural parts algebraicly related in the same manner as every other elliptical shape. That is: there is a constant for ellipses as their is "pi" for circles.

Now, find the exact Golden Ratio within said circle.

Last edited:
Jimmy Snyder
brunardot said:
I'll accept your solution, as my given statements are difficult to construe.

I would prefer:

1 = perigee
0 = soliton (half a wave or half the focal length)
1 = vector (line from a focus to the end of the minor diameter)
1 = apogee
2 = major diameter.

I prefer my own answer because it is difficult to misconstrue. What do you mean by soliton? What do you mean by half a wave?

brunardot
Solution now rejected.

jimmysnyder said:
I prefer my own answer because it is difficult to misconstrue. What do you mean by soliton? What do you mean by half a wave?

jimmysnyder said:
0 - the distance between the two foci *
1 - the distance from the center to the ellipse along the minor axis *
1 - the distance from the center to the ellipse along the major axis *
2 - the diameter

where * means "Treating the circle as a special case of an ellipse"

Note that I switched 'minor' and 'major' from what I had originally posted.

Now that you have clarified your position, I admit to being overly generous. And, I have, thus, decided to reject your solution for the following three reasons:

1.) The radius of a circle is ambiguous when referring to a special ellipse.

2.) ”The distance between the two foci” is wrong. To be consistent with the analogy, it should be: half the distance between the foci.

3.) Your subsequent switching of the minor and major axes was a good move. However, neither is correct. To be consistent with the analogy, the first should be: the distance from a focus and an end of the minor diameter. The second should be: the apogee (the distance from a focus to the furthest end of the major diameter)

I prefer to think of the focal length as a wave length; therefore the term “wave”; thus, half a wave (the distance from the center to a focus) is referred to as a: soliton. What was not clear in my prior post other than your confusion?

Last edited:
Jimmy Snyder
brunardot said:
I prefer to think of the focal length as a wave length
Can you define the focal length of an ellipse for me please?

brunardot
Sorry

jimmysnyder said:
Can you define the focal length of an ellipse for me please?

Sorry, I forgot that there were other interpretations.

I was referring to the distance between the foci.

Sorry, if I confused.

Jimmy Snyder
brunardot said:
1 = perigee
0 = soliton (half a wave or half the focal length)
1 = vector (line from a focus to the end of the minor diameter)
1 = apogee
2 = major diameter.

Are you saying that for the general ellipse:

vector = perigee + soliton
apogee = soliton + vector
major diameter = vector + apogee

brunardot
?

jimmysnyder said:
Are you saying that for the general ellipse:

vector = perigee + soliton
apogee = soliton + vector
major diameter = vector + apogee

You're very good at cutting to the crux.

Actually, the major diameter equals 2v or p + a.

Last edited:
Jimmy Snyder
brunardot said:
You're very good at cutting to the crux.

brunardot
??

jimmysnyder said:

What part of the below answer do you not understand?

"Actually, the major diameter equals 2v or p + a."

It was a statement concerning the situation; not intended as flattery.

Last edited:
Jimmy Snyder
brunardot said:
major diameter equals 2v or p + a

Yes, I am aware of this equation. But repeating this equation does not answer my question. I was asking if the following is true:

major diameter = vector + apogee

I would expect an answer along the lines of either yes, or no.

I am also asking if the following are true:

vector = perigee + soliton
apogee = soliton + vector

Yes or no would do nicely here as well. My questions are not arbitrary, I want to know because you seem to be calling this sequence a revised Fibonacci sequence (post #9 in this thread):

perigee, soliton, vector, apogee, major diameter.

brunardot
I believe I understand the confusion

I believe that now I understand the confusion.

jimmysnyder said:
Yes, I am aware of this equation. But repeating this equation does not answer my question. I was asking if the following is true:

major diameter = vector + apogee

I would expect an answer along the lines of either yes, or no.

No.

I stated: "the major diameter equals 2v (2 times vector) or p + a (I usually refer to the apogee as "o" because "a" is the amplitude; thought this would confuse, so used "a"; however, with that: p + o, the perigee plus apogee equals the major diameter."

jimmysnyder said:
I am also asking if the following are true:

vector = perigee + soliton
apogee = soliton + vector

Yes or no would do nicely here as well.

Yes.

When I made no mention, I had intended to indicate these were correct.

jimmysnyder said:
My questions are not arbitrary, I want to know because you seem to be calling this sequence a revised Fibonacci sequence (post #9 in this thread):

perigee, soliton, vector, apogee, major diameter.

I appreciate your questions; did not intend to imply otherwise. You have ventured where no other would.

I was not clear; the above is only true for the special ellipse, which is the circle. Only the first four terms of RFS apply to regular ellipses.

The confusion was entirely my fault. To mitigate, I have little time and monitors from other threads on my butt all day.

jimmysnyder said:

See my last sentence above.

Last edited:
Jimmy Snyder
brunardot said:
the above is only true for the special ellipse
The same can be said for my original answer (post #8 in this thread), the one you tentatively accepted and subsequently rejected:

0 - the distance between the two foci *
1 - the distance from the center to the ellipse along the minor axis *
1 - the distance from the center to the ellipse along the major axis *
2 - the diameter

where * means "Treating the circle as a special case of an ellipse"

brunardot
Yes. but . . .

jimmysnyder said:
The same can be said for my original answer (post #8 in this thread), the one you tentatively accepted and subsequently rejected:

0 - the distance between the two foci *
1 - the distance from the center to the ellipse along the minor axis *
1 - the distance from the center to the ellipse along the major axis *
2 - the diameter

where * means "Treating the circle as a special case of an ellipse"

When I first commented "No," I did not like your order of the major and minor diameters. I felt they were contrived to match the integers rather than their ascending order. (You subsequently, reversed them.)

I, also, did not like your mixing two circular terms (radius and diameter) with two elliptical terms (major and minor diameters.)

I felt there was some confusion, on your part, as to what were the corresponding circular and elliptical parts. This correspondence is more salent to general applications of the Brunardot series to ellipses; than, the RFS to circles.

The RFS is also a special case of the more general BS.

Regardless, I now feel you have a grasp of the underlying principles of the problem.

Are you ignoring; or, have you missed my earlier relation to the Golden Ratio?

Last edited:
Jimmy Snyder
brunardot said:
When I first commented "No," I did not like your order of the major and minor diameters. I felt they were contrived to match the integers rather than their ascending order. (You subsequently, reversed them.)

I, also, did not like your mixing two circular terms (radius and diameter) with two elliptical terms (major and minor diameters.)

Did not like? That is irrelevant. My post was a correct answer to the puzzle.

brunardot
I disagree

jimmysnyder said:
Did not like? That is irrelevant. My post was a correct answer to the puzzle.

I disagee; as you also have the right to.

I suspect we will need Korzybski (now dead) to referee.