The Golden Ratio (why it is so irrational) - Numberphile
video description
Date: 2022-04-09
Related videos
Comments and reviews: 9
Mr
For all the math magic, it isn't clear to me that phi is more irrational than pi. How is it any less effective to summarize phi as 1. 6 than it is to summarize pi as 3. 14? Both are pretty well captured by a rational number. In fact it seems like phi might be captured better, if you ignore the fractions and equations and just focus on the decimal solutions. I see how in the context of these point distributions it creates a more random pattern, but isn't that a somewhat arbitrary method to choose for distinguishing a number as more or less rational? What makes this method of point plotting a better judge that some other means of examining phi and pi?
reply
For all the math magic, it isn't clear to me that phi is more irrational than pi. How is it any less effective to summarize phi as 1. 6 than it is to summarize pi as 3. 14? Both are pretty well captured by a rational number. In fact it seems like phi might be captured better, if you ignore the fractions and equations and just focus on the decimal solutions. I see how in the context of these point distributions it creates a more random pattern, but isn't that a somewhat arbitrary method to choose for distinguishing a number as more or less rational? What makes this method of point plotting a better judge that some other means of examining phi and pi?
reply
Celia
Very well explained. It seems the seeds are most densely packed when they go around with this ratio. Nature knows how to maximise its efficiency! I forgot it was symbolized with a phi (capital or lower case) and what its value was, but then it's not a number I have used for anything else other than as a curiosity to occasionally look up.
reply
Very well explained. It seems the seeds are most densely packed when they go around with this ratio. Nature knows how to maximise its efficiency! I forgot it was symbolized with a phi (capital or lower case) and what its value was, but then it's not a number I have used for anything else other than as a curiosity to occasionally look up.
reply
todd
How well defined are these concepts, are there names for things like the distance between the seeds and etc? Is this a certain type of math? Phyllotaxis?
Where can I get more information? I just arrived to your planet and I am struggling to find a source that reflects the knowledge humans poses on a subject.
Thanks for the help!
reply
How well defined are these concepts, are there names for things like the distance between the seeds and etc? Is this a certain type of math? Phyllotaxis?
Where can I get more information? I just arrived to your planet and I am struggling to find a source that reflects the knowledge humans poses on a subject.
Thanks for the help!
reply
MrGriff305
I don't understand how the placement mechanism decides to increase the radius of placement when there's a conflict of seed location. This wasn't fully explained and it affects density of placement. Would a flower recognize a conflict and place the next see farther out? Do the patterns shown depend on this?
reply
I don't understand how the placement mechanism decides to increase the radius of placement when there's a conflict of seed location. This wasn't fully explained and it affects density of placement. Would a flower recognize a conflict and place the next see farther out? Do the patterns shown depend on this?
reply
Bryn. S.
Can you not have a Golden Ration type function? for every number not just 1
+ PHI = (1+sqrt( x-2. 4 + 1 )/2
&
(- PHI = (1-sqrt( x-2. 4 + 1 )/2)
PHI = ( x-2 / PHI ) + 1
PHI-2 - PHI - x-2 = 0
PHI-2 = x-2. PHI
reply
Can you not have a Golden Ration type function? for every number not just 1
+ PHI = (1+sqrt( x-2. 4 + 1 )/2
&
(- PHI = (1-sqrt( x-2. 4 + 1 )/2)
PHI = ( x-2 / PHI ) + 1
PHI-2 - PHI - x-2 = 0
PHI-2 = x-2. PHI
reply
Stoaty
Top class explaining
Thanks for the -Note on this video: Ben uses -one over a number- quite often. - bit in the description (doobiliy doo)
13: 25 you can slow this bit down with < key a few times and its kinda trippy: )
reply
Top class explaining
Thanks for the -Note on this video: Ben uses -one over a number- quite often. - bit in the description (doobiliy doo)
13: 25 you can slow this bit down with < key a few times and its kinda trippy: )
reply
MrAlec78uk
Though billions of years of everlotion flowers have made this number in there DNA (seeds) sarvival of the fitist carries on they have probly tryed every other number but went extinct, natural selection at its fineist.
reply
Though billions of years of everlotion flowers have made this number in there DNA (seeds) sarvival of the fitist carries on they have probly tryed every other number but went extinct, natural selection at its fineist.
reply
James
Pi, e, square root of 2, the golden ratio, and other important numbers in base 10 are irrational. Has anyone ever investigated whether any of these numbers are rational in other bases? Might be some insight if so.
reply
Pi, e, square root of 2, the golden ratio, and other important numbers in base 10 are irrational. Has anyone ever investigated whether any of these numbers are rational in other bases? Might be some insight if so.
reply
Jamison
Watched all this and really enjoyed it. now I'm going to watch again and code my own version. I love when mathematical concepts show some element of symmetry or beauty when you never expect it.
reply
Watched all this and really enjoyed it. now I'm going to watch again and code my own version. I love when mathematical concepts show some element of symmetry or beauty when you never expect it.
reply
Add a review, comment
Other channel videos
