h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

the law of thirds can apply and usualy does help most people keep their photos interesting. however the simple ratio of 1:2 isn't the most pleasing proportion that could be taken. the most pleasing proportion is somewhere around 1:1.618 ish. it is derived from the algebraic proportion noticed in such things as the human body, the rate at which rabbits multiply (perhaps you have studied the fibbinoci sequance, pick two sequential terms somewhere down the line a ways divide them, itl come out to an aproximation of this proportion!), the sunflower, and a bewildering list of othor natural and manmade things. this algebraic formula is A/B=B/(A+B) work it out don't forget how to multiply in and use the quadratic formula and you'll come out with this amazing number, that is a quite pleasing proportion.

I don't believe that about the golden ratio. I've done my own experiments and have shown that the actual most pleasing ratio is bigger than 1.618. The golden ratio theory was invented by people who were trying to make real life fit into their idea of perfection which was mathematics.

what kind of experiments?

I drew a few rectangles and asked people which were the nicest looking.

That's all the Golden Ratio people did. Well, they faked a few results as well to make the facts fit the theory.

what number did you come out with?

It's a long time ago, now, so I don't remember exactly. It was bigger than the golden ratio, though.

Right...

if you don't have any results then what was the point of this? you havn't proved me wrong, and there is a slough of othor reasearch that has evidence supporting 1.618 as the golden ratio. it's not just in calculations it comes up in hundreds of examples of ancient art and nature, which has always been more correct than any human.

Nah, there's almost no research done to prove that 1.618 has special properties. Everybody just quotes the fact that research was done. I don't think any research was ever done, except for the one were the guy measured women's navel heights versus body heights, and even then he faked the results. The result just goes back to the Greeks who thought that art should reflect the "perfection" of numbers, so this ratio had to look the best.

If the results go back to the Greeks, then why did the Egyptians use this proportion? In the pyramids the length of the side of the base to the height is exceptionally close to 1.618. It also shows up in their pottery, the width to the height yields 1.618. in Babylonian pyramids the same effect, in most steles of the time, the height of a post to the width of the lintel in free standing dolmans of Europe, the rate at which pairs of rabbits multiply, the number of seeds of each concentric ring of a sunflower, some trees (I forget which type, Sorry) grow leaves and branch off to this proportion, these things all came well before the Greeks came around. This number isn't just the most pleasing visual proportion, it governs many other things.

I don't dispute the existence of the Fibonacci series and the Golden Ratio in nature. But that is nothing to do with beauty.

On the use of the Golden Ratio in architecture, you have fallen into the trap of assuming that when people claim things , they are true. You should check these things for yourself.

Egyptian pyramids: The Egyptian pyramids were all different shapes and sizes, so you can't make a general claim about what ratio was used. For the most famous pyramid, the Great Pyramid, the base is 230m and the height was originally about 147m, giving a ratio of 1.56, which is not close to Phi.

What you say about Babylonian pyramids makes no sense at all, since the Babylonians didn't build pyramids.

I've no doubt that people have claimed the other things that you say, but they don't stand up examination.

bear in mind that the mesurments of the egyptian pyramids were taken after they had degraded, the babalonians did build pyramids, they were called steped pyramyds, steped mestabas, or ziggerots. and once you take in the fact that these have been worn down it raises the number you get.

It's very easy to say "we don't have accurate measurements of the pyramids, but if we did have, they would give the ratio 1.618". In fact, we have extremely accurate measurements of the Great Pyramid, which show that the ratio does not equal 1.618.

I don't know about Sumerian Ziggurats, which is what you appear to be talking about, but if they are worn away, we can't include them in our theory.

the truth is that we don't have acurate mesurments of the pyramids as they were originaly built, but our mesurments today come out low, as they should be because of the wear on the pyramids. as for the ziggerots, many of them are quite well preserved and genertate this number. but you still havn't answered any of my othor examples, one of which is the dolmans of europe, some of the oldest arcatecture in history, the most famous being stonehenge. they obviously didn't have the mathematical tools to generate this number explicitly, but their arcatecture shows it all across europe. i guess my point is that this number was generated through careful study of what past cultures found to be asteticly pleasing, which is the ratio A/B=B/(A+B). in our conversation i have only given a few light examples of what has been studied, but rest assured there are multitudes more.

1. We have have extremely accurate measurements of the base of the great pyramid, down to about one tenth of an inch, since the original cornerstones are still in place and have not worn at all since they were buried in sand for thousands of years. Just look at Flinders Petrie's measurements for details. We also have a very good estimate of the height of the pyramid based on the angle of those same corner stones, which shows conclusively that the ratio was never 1.618.

The fact that you keep insisting it was shows that you are not interested in the facts, here, only in the idea that Phi was used.

2. I don't know about the Ziggurats as I said before.

3. I have studied dolmens of Europe and they definitely do not exhibit Phi in any way.

4. I have also studied Stonehenge, which is not a dolmen, in detail. About eight of the original stones have amazing alignments with the sun and moon, all of which you'll find I put into the Stonehenge Entry, but Phi doesn't appear anywhere there either.

The truth is that you don't understand any of these examples you are quoting, so I'm really not prepared to discuss this further.

OK so I looked at the measurements of the pyramids and it is an approximation of the golden ratio, when you do calculate it out it does come to 1.5757, the other two pyramids come to 1.5772 and 1.6030(citing NOVA for the numbers, it's fair to say public television is reputable). All of which are accurate to within five HUNDRETHS! I think on this scale five hundredths is quite reasonable. BUT remember this isn't even the issue here. I'm not here to argue about the pyramids I simply made the statement that 1.618 is the golden ratio, if this is what you wish to argue you need to provide evidence to the contrary, not just naysay anything I assert. You attempted to do so with one of my propositions but in doing so you came out with a number less that mine, but in an earlier post you said that it should be higher. I know you’re thinking that the Egyptians didn't use the golden ratio because they didn't know about it. This is true but I can say with some confidence that they tried to make them in an astatically pleasing way. That is what makes me think that this is a good way of attempting to estimate the number we are looking for in an astatically pleasing ratio. Many of the dolmans of Europe do show this intriguing property, not all and I never said all (and actually Stonehenge only shows it in a few select places, but they are obscure and the measurements aren't from reputable sources, I just quoted that one because it is the most famous and for the unsophisticated reader it would give them an idea of what I was talking about), but you would be surprised where it pops up when you know what you're looking for. I can show many examples of the golden ratio in modern architecture and art, but these were after the number was discovered, and therefore not made with the inspiration for beauty but in attempting to use our knowledge to make our art more beautiful. With the examples I have given I am attempting to refute your proposition that it was a number the Greeks came up with. We can move on with this argument, but with your eagerness to end this conversation, I’m not expecting a reply.
Your loss...

It's rude of me to stamp out in the middle of the conversation; you've been polite, so I should be too.

I'll try and answer.

I'm not saying you are wrong about the golden ratio in every way. I'm saying that you are putting together a lot of conflicting claims, with very little or no evidence.

There are three or four things at issue here:

1. The golden ratio A2346374 is a mathematical number, which is the limiting ratio of adjacent elements of the Fibonacci series.

2. The Fibonacci series has been found in nature, in plant growth: seeds in a sunflower and leaf buds arranged around a stalk are two examples - I don't know the botanists' technical names for these.

3. The golden ratio was known to the Ancient Greeks - since the Ancient Greeks who wrote down the mathematics (Euclid and friends) lived in Egypt, it is likely that the Egyptians also knew about it at the time (300 BC). This doesn't say anything about whether the Ancient Egyptians (2700 BC) knew about it.

4. The Greeks didn't call it the Golden Ratio (they called it extreme and mean ratio) and they made no claims about its beauty or pleasingness.

5. The first claims about the pleasing aspects of the Golden Ratio were made in the 18th Century (I think - it might have been the 19th).

6. Did the Ancient Egyptians use the golden ratio in designing the pyramids? Apparently not. The five percent you quote may appear close, but the Egyptians were much better builders than you give them credit - they could build to an accuracy of about 0.1% so 5% is way out. So I claim they were not using the golden ratio by design.

7. Were they using it subconsciously? It's hard to say, but the figures for the pyramids don't seem bear it out: the first pyramids were much steeper, then it was found that they kept collapsing, so they made them "fatter". Khafre's pyramid appears to have been made steeper so that it would match Khufu's (the Great Pyramid A623611) in height and appear as imposing, even though it contains far less material (and as a result was less expensive to build). Other pyramids have a whole range of different slopes.

8. Dolmens A3181673 are made from very rough stones - one of the features of them is that the stones are not worked into flat surfaces. They are just dug out of the ground and erected into the tripod shape. So it is not realistic to say that they exhibit any ratio - there's no way you can measure them accurately.

9. I'd be interested in hearing where Stonehenge A9564942 shows the golden ratio, as I didn't find it in any of my own studies of it, for the Stonehenge entry.

10. It is very easy if you search long enough to find pictures that show the golden ratio, but there are lots of pictures that don't. If you want to be scientific about it, you have to see is there a significant number that do. I don't think anybody has ever done this. They've just produced a few pictures and claimed it is a fundamental principle of art. This is not science, and does not deserve to be reported in every book on mathematics.