The Golden Ratio

**Rotary** · 01-31-2006, 08:38 PM

I searched up what I put as the subject name (The Golden Ratio) and oh well, I decided to make it a thread. But, do you think that the spiral in the labyrinth, since it is described as somewhat 'never ending' when he throws the glow stick down [and the glow just fades], that it may deal with the Golden Ratio? Not that it deals with it, but it relates to it because it's never ending, as also the Golden Ratio is never ending. On the cover of the book, the spiral is drawn somewhat like it. Am I stupid for thinking that? I started studying the Golden Ratio just for my own pleasure, and it reminded me of this, any thoughts, ideas, or comments?

**fearful_syzygy** · 01-31-2006, 09:05 PM

“Bingo.” Langdon began racing through slides now — spiraled pinecone petals, leaf arrangement on plant stalks, insect segmentation — all displaying astonishing obedience to the Divine Proportion.
“This is amazing!” someone cried out.
“Yeah,” someone else sad, “but what does it have to do with art?”
“Aha!” Langdon said. “Glad you asked.” He pulled up another slide — a pale yellow parchment displaying Leonardo da Vinci's famous male nude — The Vitruvian Man — named for Marcus Vitruvius, the brilliant Roman architect who praised the Divine Proportion in his text De Architectura.
“Nobody understood better than Da Vinci the divine structure of the human body. Da Vinci actually exhumed corpses to measure the exact proportions of human bone structure. He was the first to show that the human body is literally made of building blocks whose proportional ratios always equal PHI.”
Everyone in class gave him a dubious look.
“Don't believe me?” Langdon challenged. “Next time you're in the shower, take a tape measure.”
A couple of football players snickered.
“Not just you insecure jocks,” Langdon prompted. “All of you. Guys and girls. Try it. Measure the distance from the tip of your head to the floor. Then divide that by the distance from your belly button to the floor. Guess what number you get.”
“Not PHI!” one of the jocks blurted out in disbelief.
“Yes, PHI,” Langdon replied. “One-point-six-one-eight. Want another example? Measure the distance from your elbow to your fingertips. PHI again. Another? Hip to floor divided by knee to floor. PHI again. Finger joints. Toes. Spinal divisions. PHI. PHI. PHI. My friends, each of you is a walking tribute to the Divine Proportion.”
Even in the darkness, Langdon could see they were all astounded.

**sutrix** · 02-01-2006, 01:23 AM

Ellimist loves you.

**Rotary** · 02-02-2006, 03:53 PM

Ohh, okay...

**Centaure** · 02-03-2006, 07:38 AM

Damn ! f_s is polluting ! He's been in enemy territories !

**FasTBird232** · 02-03-2006, 10:18 AM

Quote:

Originally Posted by fearful_syzygy

“All of you. Guys and girls. Try it. Measure the distance from the tip of your head to the floor. Then divide that by the distance from your belly button to the floor. Guess what number you get.”
“Not PHI!” one of the jocks blurted out in disbelief.
“Yes, PHI,” Langdon replied. “One-point-six-one-eight. Want another example? Measure the distance from your elbow to your fingertips. PHI again. Another? Hip to floor divided by knee to floor. PHI again.

I tried it.

Head to floor: 70 inches
Belly button to floor: 42 inches
70 / 42 = 1.67

(the second one doesn't make any sense, as it only asks for one measurement)

Hip to floor: 40 inches
Knee to floor: 22 inches
40 / 22 = 1.81

You could pick and choose dozens of lenghts on your body that would work out to a 1.69 ratio, though.

For what it's worth.

**Slow Dog Noodle** · 02-03-2006, 10:56 AM

Fascinating. I think we’re on to something here…

**fearful_syzygy** · 02-03-2006, 11:06 AM

“Gentlemen,” he said, “I invite you to go and measure that kiosk. You will see that the length of the counter is one hundred and forty-nine centimetres — in other words, one hundred-billionth of the distance between the earth and the sun. The height at the rear, one hundred and seventy-six centimetres, divided by the width of the window, fifty-six centimetres, is 3.14. The height at the front is nineteen centimetres, equal, in other words, to the number of years of the Greek lunar cycle. The sum of the heights of the two front corners and the two rear corners is one hundred and ninety times two plus one hundred and seventy-six times two, which equals seven hundred and thirty-two, the date of the victory of Poitiers. The thickness of the counter is 3.10 centimetres, and the width of the cornice of the window is 8.8 centimetres. Replacing the numbers before the decimals by the corresponding letters of the alphabet, we obtain C for ten and H for eight, or C10H8, which is the formula for naphthalene.”
“Fantastic,” I said. “You did all these measurements?”
“No,” Agliè said. “They were doe on another kiosk, by a certain Jean-Pierre Adam. But I would assume that all lottery kiosks have more or less the same dimensions. With numbers you can do anything you like. Suppose I have the sacred number 9 and I want to get the 1314, date of the execution of Jacques de Molay — a date dear to anyone who, like me, professes devotion to the Templar tradition of knighthood. What do I do? I multiply nine by one hundred and forty-six, the fateful day of the destruction of Carthage. How did I arrive at this? I divided thirteen hundred and fourteen by two, by three, et cetera, until I found a satisfying date. I could also have divided thirteen hundred and fourteen by 6.28, the double of 3.14, and I would have got two hundred and nine. This is the year in which Attalus I, king of Pergamon, joined the anti-Macedonian League. You see?”

**John B.** · 02-03-2006, 11:17 AM

Quote:

Originally Posted by fearful_syzygy

“Gentlemen,” he said, “I invite you to go and measure that kiosk. You will see that the length of the counter is one hundred and forty-nine centimetres — in other words, one hundred-billionth of the distance between the earth and the sun. The height at the rear, one hundred and seventy-six centimetres, divided by the width of the window, fifty-six centimetres, is 3.14. The height at the front is nineteen centimetres, equal, in other words, to the number of years of the Greek lunar cycle. The sum of the heights of the two front corners and the two rear corners is one hundred and ninety times two plus one hundred and seventy-six times two, which equals seven hundred and thirty-two, the date of the victory of Poitiers. The thickness of the counter is 3.10 centimetres, and the width of the cornice of the window is 8.8 centimetres. Replacing the numbers before the decimals by the corresponding letters of the alphabet, we obtain C for ten and H for eight, or C10H8, which is the formula for naphthalene.”
“Fantastic,” I said. “You did all these measurements?”
“No,” Agliè said. “They were doe on another kiosk, by a certain Jean-Pierre Adam. But I would assume that all lottery kiosks have more or less the same dimensions. With numbers you can do anything you like. Suppose I have the sacred number 9 and I want to get the 1314, date of the execution of Jacques de Molay — a date dear to anyone who, like me, professes devotion to the Templar tradition of knighthood. What do I do? I multiply nine by one hundred and forty-six, the fateful day of the destruction of Carthage. How did I arrive at this? I divided thirteen hundred and fourteen by two, by three, et cetera, until I found a satisfying date. I could also have divided thirteen hundred and fourteen by 6.28, the double of 3.14, and I would have got two hundred and nine. This is the year in which Attalus I, king of Pergamon, joined the anti-Macedonian League. You see?”

Okay--what's truly strange about this is the fact that you have so little to do over there in grad-school land that you have time to do this sort of stuff.

I also liked reading "doe" as "d'oh!" in a passage like this.

**fearful_syzygy** · 02-03-2006, 11:35 AM

Well obviously I didn't have time to proofread it properly.

Nose to the grindstone and all that.

In what way weirded out?

**John B.** · 02-03-2006, 03:22 PM

Not "weirded out"--I misspoke.

I've changed my previous post to more accurately reflect my thinking.

**sutrix** · 02-03-2006, 08:00 PM

Quote:

Originally Posted by fearful_syzygy

Well obviously I didn't have time to proofread it properly.

You typed all that up?

I thought you downloaded an e-book and copy-pasted. That'd at least be a minor rebellion.

**fearful_syzygy** · 02-03-2006, 08:06 PM

All that what? It took me ten minutes at most.

Besides, there is a long tradition of posting passages from Foucault's Pendulum around here, and that happens to be one of my favourites.

**sutrix** · 02-03-2006, 08:22 PM

Tha Langdin passige, mon.

**zakalwe** · 02-04-2006, 12:20 AM

Quote:

Originally Posted by sutrix

Tha Langdin passige, mon.

Surely "The Brown Passage"?

Oh.

That's a great 2nd quote F_S, and almost enough to get me to read FP. I'd need some cider first, tho.

**naught** · 02-04-2006, 02:44 AM

**g@rp** · 02-04-2006, 04:00 AM

Modulor of Le Corbusier.

**bigm141414** · 02-20-2006, 06:45 AM

for those who are interested the golden ratio also shows up in the characteristic impedance of a resistive ladder network, such that Zin=1.618*R

I thought it was cool but then again i am dork.

**heartbreak** · 07-28-2007, 10:57 PM

Golden rectangles can be found by multiplying their short side by 1.62 to get their long side.

If you remove the square of the short side from the rectangle you end up with another golden rectangle, thus can be done infinitely and can be used to approximate a golden spiral.

If opened up and laid flat, like House of Leaves so conveniently does, it forms a rectangle with the short side measuring 9 1\4 inches. (All measurements taken off a full color paperback.)

9.25 x 1.62 = 14.985

The back cover is 7 inches wide. The book is 1 1\4 inches thick and the front cover is 6 1/2 inches wide.

7 + 1.25 + 6.5 = 14.75

1\4" inch short.

**Ellimist** · 07-29-2007, 08:10 AM

I measure the back to be 6 ¹⁵/₁₆ in.... however, this is on a blue edition, for I do not have my color at the moment... The same is true for the red.

Hrm... I get 9 ³/₁₆ in. for the short side. (9.1875 * 1.6180339887 = 14.86568727118125)

Edit: That took too long to understand. I see what you did there. You measured directly with the cover and then added to get the open length. Heh. I have a problem with the thickness measurement for the sides. when the book is open, the thickness more than doubles past 2 inches because it is stretched out, of course, this is dependent on how flat you press the book.

Using your measurements with my phi:

9.25 * 1.6180339887 = 14.966814395475

Measuring the lengths:

7 + 1.25 + 6.5 = 14.75

14.966814395475 - 14.75 = 0.2168

Not 1/4"?

I think it is a very rough approximation, but it makes sense that it would make a golden spiral. However, the front cover thing - I measured it to be 7/16 shorter than the full width of the pages (6 and 15/16 in.)

The roughness is the worst with the thickness measurements.

**heartbreak** · 07-29-2007, 11:13 AM

Not a hell of a lot of difference between 15, 14.985, and 14.966814395475.

or for that matter 0.2168 and .25.

Close enough to be manufacturing discrepancies. Its not as though they could machine the book down to exact tolerances.

But you are correct, it is not exact.

**Ellimist** · 07-29-2007, 11:19 AM

Quote:

Originally Posted by heartbreak

Close enough to be manufacturing discrepancies. Its not as though they could machine the book down to exact tolerances.

Yeah... that is what I was thinking about.

If MZD wanted his book to be formed in the way you described, then he probably succeeded. I am just not sure how perfect printing presses can make books to measurement.

**heartbreak** · 07-29-2007, 11:47 AM

Essentially, no matter where the book is opened, the reader is staring down a spiral

**heartbreak** · 07-29-2007, 12:09 PM

I found ftaires!!!

**Ellimist** · 07-29-2007, 12:26 PM

Nice! I like it.

**Ellimist** · 08-26-2007, 08:43 AM

Ha... check this out:

http://www.duggmirror.com/design/A4_vs_US_Letter

**heartbreak** · 08-26-2007, 11:06 AM

Thats pretty cool, Ell. Have you tried applying it to the book to see if matches up the same?

**Ellimist** · 08-26-2007, 11:16 AM

Unfortunately, I have not...

**heartbreak** · 03-19-2008, 06:20 AM

While not quite golden, this ratio is extremely strange. As we have found in Virginia there are two Ash Tree Lanes. One in suburbia and one out in the country. The latter one also intersects with Echo Hill Road and adds a nice touch. It is also close to Roanoke which has been discussed on this forum as well. If I'm remembering right, Roanoke was a colony that kept disappearing. Close to Roanoke is Lynchburg home of Rudolf Women's College. Pearl S Buck attended there. Tad Z Danielewski directed a movie that she wrote. Also, in the library there at Rudolf is the Nora Stirling Collection. A collection of stuff pertaining to Pearl S Buck. Including letters between her and Tad Danielewski.

The distance between Ash Tree Lane and Roanoke is approximately 140.55 miles and from Ash Tree Lane to Lynchburg is 106.71 miles.

106.71/140.55 is approximately 0.759231

The height of House of Leaves is roughly 9 and a quarter inches and the width is roughly 7 inches.

7/9.25 is approximately 0.756756

That's one crazy coincidence to have those ratios come out so close.

**heartbreak** · 03-19-2008, 04:04 PM

Not quite the same ratio, but still pretty close.

Ash Tree Lane to LA 2240.92 miles.

Ash Tree Lane to Flagstaff 1860.08 miles.

1860.08/2240.92 is approximately 0.830051

Ash Tree Lane to Seattle 2282.06.

1860.08/2282.08 is approximately 0.815088