Im just starting this topic because my Trig./Pre-Calc. class was researching the Golden Ratio the past couple of days.
Just in case you dont know what the Golden Ratio, it is one half the value of 1 plus the square root of 5, or about 0.618...
Heres a couple things that I remember off the top of my head:
1. Stradivarius's Violins were designed using the Golden Ratio
2. There is a type of saxophone mouthpiece that uses the Golden Ratio for its proportions and apparently has a superior sound quality.
3. The training recording studio at the Recording Institute of Detroit is dubbed the "Golden Section Studio." This is because it is in the shape of a golden rectangle and every room inside the studio is a golden rectangle. Apparently the actual recording room has superior accoustics. For instance the reverberations are almost exactly the same pitch as the original sound.
4. There is a sound company that makes a patented type of speaker wire. This wire's individual wire strands are different sizes based on the Golden Ratio. With the wire's design it cancels out the small vibrations caused by electricity flowing through the wire. This, in turn, produces very naturally accurate sound.
If anyone has any more information (and I know there is more) please post it for the people who dont know as much about the implications of the Golden Ratio (Phi (Fibonacci Sequence)).
In theory all of the parts of the human body are in perfect ratio: 1:Phi e.g. the width between chin and the upper lip and the length of the nose. This is really call because it applies to nearly all parts of the body; the hands the arms the legs etc.
| llobo1 wrote: |
| In theory all of the parts of the human body are in perfect ratio: 1:Phi e.g. the width between chin and the upper lip and the length of the nose. This is really call because it applies to nearly all parts of the body; the hands the arms the legs etc. |
It's a good theory but it is almost never true in reality....try measuring yourself.It's also said that photographs and art designed to the Golden Ratio (eg. with the subject in the smallest rectangle (?) they are the most pleasing to the eye.
| Bikerman wrote: |
| llobo1 wrote: | | In theory all of the parts of the human body are in perfect ratio: 1:Phi e.g. the width between chin and the upper lip and the length of the nose. This is really call because it applies to nearly all parts of the body; the hands the arms the legs etc. |
It's a good theory but it is almost never true in reality....try measuring yourself. |
Actually if you try it the different parts of your body are actually normally very close to being in perfect proportion (we tried this in maths once). But this is meant to apply to the perfect person. | llobo1 wrote: |
| Bikerman wrote: | | llobo1 wrote: | | In theory all of the parts of the human body are in perfect ratio: 1:Phi e.g. the width between chin and the upper lip and the length of the nose. This is really call because it applies to nearly all parts of the body; the hands the arms the legs etc. |
It's a good theory but it is almost never true in reality....try measuring yourself. |
Actually if you try it the different parts of your body are actually normally very close to being in perfect proportion (we tried this in maths once). But this is meant to apply to the perfect person. |
It depends what you mean by close. The best way to measure that would be to carry out a standard deviation calculation. There is, perhaps, a very good science project here for anyone who is looking for an interesting experiment to do.I remember finding out about the golden ratio when I was looking at fibinucci sequences. I was thinking about it like so:
F(0) = A
F(1) = B
F(2) = A+B
F(3) = F(1)+F(2)
E.Q. F(X+2)=F(X)+F(X+1)
I wondered whether there was a ratio between F(X+1) / F(X). So,
F(X+2) = F(X+1) * R
What does that ratio eventually work out to be? The golden ratio.
| indeedwrestling wrote: |
I remember finding out about the golden ratio when I was looking at fibinucci sequences. I was thinking about it like so:
F(0) = A
F(1) = B
F(2) = A+B
F(3) = F(1)+F(2)
E.Q. F(X+2)=F(X)+F(X+1)
I wondered whether there was a ratio between F(X+1) / F(X). So,
F(X+2) = F(X+1) * R
What does that ratio eventually work out to be? The golden ratio. |
The introduction of A and B would seem unnecessary since they have fixed values of 0 and 1. The more concise way of expressing it would be :
You cannot express this as you have done above, it is mathematically incorrect. To demonstrate this, solve it for the value x=1. Your solution gives
F(3) = F(2) * 1.618
since F(2) = 1 therefore F(3) = 1.618
contra-hyp.
Here is another way to think about it which does work...
The golden ratio can be thought of as the positive solution to the quadratic:
x^2-x-1=0 = (1+SQRT(5))/2 = ð = 1.618 (approx)
Using the closed form solution to the above, you arrive at the solution:
F(x)= (ð^x-(1-ð)^x/sqrt(5)
This is known as Binet's formula...
There is a proof of this at: http://en.wikipedia.org/wiki/Fibonacci_number | Bikerman wrote: |
| llobo1 wrote: | | Bikerman wrote: | | llobo1 wrote: | | In theory all of the parts of the human body are in perfect ratio: 1:Phi e.g. the width between chin and the upper lip and the length of the nose. This is really call because it applies to nearly all parts of the body; the hands the arms the legs etc. |
It's a good theory but it is almost never true in reality....try measuring yourself. |
Actually if you try it the different parts of your body are actually normally very close to being in perfect proportion (we tried this in maths once). But this is meant to apply to the perfect person. |
It depends what you mean by close. The best way to measure that would be to carry out a standard deviation calculation. There is, perhaps, a very good science project here for anyone who is looking for an interesting experiment to do. |
Yes I agree, it does depend on what is meant by close. However, Phi does show the proportions, and many pieces of art use Phi in order to try and get the proportions right. I think that Da vinci's vitruvian man uses these proportions. | llobo1 wrote: |
| Yes I agree, it does depend on what is meant by close. However, Phi does show the proportions, and many pieces of art use Phi in order to try and get the proportions right. I think that Da vinci's vitruvian man uses these proportions. |
True. It also begs the question which has been central in maths for a long time. Is maths entirely a 'creation' or is there an underlying principle or system in the universe which is, inherently, mathematical? The debate is traditionally known as the Platonic debate after Plato who held the latter view. | Bikerman wrote: |
| llobo1 wrote: | | Yes I agree, it does depend on what is meant by close. However, Phi does show the proportions, and many pieces of art use Phi in order to try and get the proportions right. I think that Da vinci's vitruvian man uses these proportions. |
True. It also begs the question which has been central in maths for a long time. Is maths entirely a 'creation' or is there an underlying principle or system in the universe which is, inherently, mathematical? The debate is traditionally known as the Platonic debate after Plato who held the latter view. |
very interesting. Maybe someone should start a thread about this. | llobo1 wrote: |
| Bikerman wrote: | | llobo1 wrote: | | Yes I agree, it does depend on what is meant by close. However, Phi does show the proportions, and many pieces of art use Phi in order to try and get the proportions right. I think that Da vinci's vitruvian man uses these proportions. |
True. It also begs the question which has been central in maths for a long time. Is maths entirely a 'creation' or is there an underlying principle or system in the universe which is, inherently, mathematical? The debate is traditionally known as the Platonic debate after Plato who held the latter view. |
very interesting. Maybe someone should start a thread about this. |
By all means. I suspect that it would be best done in the philosophy forum. It's a close call but my own opinion is that maths is best dealt in philosophy since maths itself is not a science. It is, of course, the universal language of science but it is more than that. Many mathematicians would argue that math is something distinct and 'unto itself' as well as being just a formal language. They get quite annoyed when math is talked about in terms of it's practical uses and applications. I understand their point. There is an inherent beauty in math which may or may not reflect reality in some way and any utilitarian or practical requirements should be secondary. I am old-fashioned enough to support this viewpoint since I have always believed that knowledge for it's own sake is a good thing. There is an understandable tendency nowadays to regard knowledge in terms of it's practical contribution to society (characterised by the 'what use is it?' question). Many Universities in the UK, for example, now offer what they call 'vocational degrees'. To me that is a contradiction in terms. I always understood a degree to be a qualification in a field or discipline, not a qualification for work. I understand why many support the change. Intellectual qualifications have always been perceived as 'superior' to practical skills and qualifications. Personally I believe that to be a nonsense but the fact is that the discrimination does exist.
My own opinion is that reclassifying qualifications is not the way to tackle the issue, even though I sympathise with the aims. An undergraduate should be educated, in the literal sense of the word - ie they should be 'led towards the light'. That may or may not coincide with acquiring the skills and knowledge necessary for a particular job but it should certainly not be based on that aim.
