I believe the geometric proportion served the Creator as an idea when He introduced the continuous generation of similar objects from similar objects. -- Johannes Kepler

The Golden Ratio can be obtained easily by the proper division of a line segment, instead of constructing the geometrically pleasing rectangles. Simply divide the line segment into two parts of uneven lengths, so that the ratio of the smaller part to the larger part equals the ratio of the larger part to the entire line segment.

```       1         x
•-------•-----------•
A       B           C
```
And thus:
```         AB   BC         1     x
-- = --    or:  - =  ---
BC   AC         x    1+x

x2 - x - 1 = 0

x = (1 ± √5)/2
```
Following on from what mblase said: You can draw a series of squares inside a 'golden ratio rectangle' that theoretically goes on forever. If you keep turning the paper clockwise, and then always draw the square on the left, you can then draw a spiral through the diagonally opposite corners of the squares. This is known as the golden spiral.

```+--------------+--------+
|              |        |
|              |        |
|              |        |
|              |        |
|              +-++-----+
|              +-++     |
|              |  |     |
+--------------+--+-----+
^
Start here.```
This particular spiral is yet another example of the golden ratio in nature; many of the most attractive seashells describe this shape.

Although, let me offer a disclaimer here; just because a fair amount of natural shapes fit the golden ratio, this does not give it some kind of magical or religious significance. It could well be that a lot of seashells adopt the 'golden ratio spiral' simply because it is the easiest to build - after all, DNA is known to often create things with a fractal or recursive nature, and the golden ratio is recursive by definition.

Still, a lot of things need to be learnt about the golden ratio. Why do we find it so attractive? Is it because our faces, too, fit this ratio? (With our eyebrows and chin forming the square within the recangle, might I add). Or is this just coincedence? Don't expect an answer anytime soon...

The Golden Ratio (also known as the Golden Mean or the Divine Proportion) is best visualized using the Golden Rectangle, an otherwise ordinary rectangle whose length is slightly greater than its height. For convenience, we'll set the shorter side equal to one unit (inch, meter, furlong, whatever you like), and the longer side equal to Φ (capital Phi) units.

```   ------------------------
|                        |
|                        |
1 |                        |
|                        |
|                        |
------------------------
Φ
```

Draw a line through this rectangle such that a perfect square is on one side, leaving a smaller rectangle on the other side.

```   ------------------------
|             |          |
|             |          |
1 |             |          | 1
|             |          |
|             |          |
------------------------
1          Φ-1
```

Now, the Golden Ratio is considered "golden" because the larger rectangle and the smaller one are geometrically similar -- that is, they possess equal proportions. Expressed mathematically:

``` Φ      1
--- = -----
1     Φ-1
```

Cross-multiply to get Φ(Φ-1) = 1, or Φ2-Φ-1=0. Applying the quadratic formula to this equation (and throwing out the negative root, since we're dealing with real-world geometry) leaves us with:

Φ = (1+√5)/2

...which is approximately 1.618(03398874989484820458683436563811...). Φ-1 (the inverse of Φ) is common enough to receive its own symbol: φ (lower-case phi).

The ancient Egyptians believed that this "sacred ratio" was important enough to embed in their art and constructions. Many Egyptian temples employ rectangluar archways designed according to the Golden Ratio. At the Great Pyramid of Giza, the ratio of the length of one side of the base to the perpendicular height of the pyramid is about 2/√Φ, making the slant height of the pyramid side proportionately equal to Φ. The result is that each side of the pyramid is a Golden Triangle.

A Golden Triangle is similar to a Golden Rectangle in its behavior. It's an isoceles triangle with angles measuring 36°, 72° and 72°. It can be created from a regular pentagon by drawing lines from any vertex to the two vertices opposite it. If the base of this triangle (the short side) is Φ units long, the other two sides are 1+Φ units long. By bisecting one base angle of the triangle, two more isoceles triangles are produced and the smaller one is another Golden Triangle:

```         /\
/  \
/    \
/      \ Φ
1+Φ /        \
/         _\
/    Φ __--  \
/   __--       \ 1
/__--            \
/-_________________\
Φ
```

More famously, Aristotle and the ancient Greeks believed that rectangles possessing the Golden Ratio were inherently aesthetic. The Parthenon, for example, is constructed in such a way that the front of the temple is exactly contained in a Golden Rectangle, and the "dividing line" mentioned above lying on either side of the entryway.

Drawing these Golden figures by hand is difficult, since the Golden Ratio is an irrational number, a never-ending decimal. However, it's fairly easy to draw it using a straightedge and compass. First draw a short vertical line segment (of, say, length 1) and at one end draw a second segment perpendicular to it which is twice as long (length 2):

```  |
|
|
|
2 |
|
|
|
|
---------
1
```

Connect the endpoints to form a right triangle; the hypotenuse of this triangle is of length √5. Draw an arc centered at the point where the short side meets the hypotenuse, dividing the hypotenuse into two segments of length 1 and √5-1. Finally, draw a second arc centered at the point where the longer side meets the hypotenuse, with the radius equal to the longer section of the hypotenuse, and mark where it crosses the longer side:

```  |\
| \
|  \
|   \
|    \
|_ __-\
| /    \ 1
|/      \
|        \
---------
1
```

The longer side is divided into two lengths, one measuring √5-1 and the other 2-(√5-1) = 3-√5. The ratio of the first number to the second is exactly (1+√5)/2 -- the Golden Ratio, Φ.

Armed with this, we can now illustrate the Golden Ratio using a single line segment divided in two, known as a Golden Section. Rewriting the equation Φ2-Φ-1=0 tells us Φ2 = Φ+1, or visually:

```               Φ2
___________|___________
/                       \
*--------------*----------*
\_____ ______/ \___ ____/
|            |
Φ            1
```

(It's an interesting property of the Golden Ratio that Φ-1 = 1/Φ and Φ+1 = Φ2.) The ratio of 1 to Φ is algebraically equal to the ratio of Φ to Φ2, and so the geometric definition of the Golden Ratio is preserved: "the smaller is to the larger, what the larger is to the whole."

However, it's more interesting to see the implications of the Golden Ratio when rectangles are used. Since the Ratio remains constant no matter what the actual size of the rectangle is, the smaller rectangle is just as Golden as the larger one. We can subtract another square from it, and so continue ad infinitum:

``` --------------------------
|                 |        |
|                 |        |
|                 |        |
|                 |--------|
|                 |--|     |
|                 |  |     |
--------------------------
```

If you begin from the lower-left vertex of the largest rectangle and draw a spiral through the vertex of every smaller square, you can continue until the squares become infinitely small. Interestingly, you can create the same spiral by tracing the vertices of a series of Golden Triangles.

This spiral is known as the Golden Spiral, a specific example of the equiangular or logarithmic spiral which occurs often in nature. A cross section of a nautilus shell reveals a similar (but not identical) logarithmic spiral, as does the position of seeds in a sunflower or pine cone or the stars in a spiral galaxy.

This is not entirely a coincidence, because the Golden Ratio is also closely tied to the Fibonacci numbers. A sequence of Fibonacci numbers is constructed by beginning with any two numbers (but typically 1 and 1) and adding them to produce a third, then adding the second and third to produce the fourth, and so on: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc. As this sequence continues, the ratio between any number and the number before it rapidly approaches the Golden Ratio: 34/21 = 1.6190..., 55/34 = 1.6176..., and 89/55 = 1.6182....

We may represent the Fibonacci sequence geometrically by drawing two squares with sides 1 unit in length side by side, forming a rectangle of sides 1 and 2. Add a 2-unit square beside this to form a rectangle of sides 2 and 3. Add a 3-unit square to make a 3-by-5 rectangle, a 5-unit square to make a 5-by-8 rectangle, and so on in a spiral shape. As the squares get larger and larger and the sequence continues, the rectangles become more and more Golden and the spiral more and more logarithmic:

```   _________
|         |
|         |
|         |
8 |         |
|_____ _2_|
|   1 |_|_|
|     |   | 3
|_____|___|
5
```

This is tied to another, less algebraic representation of the Golden Ratio using infinite series. In the Fibonacci series, the ratio between successive numbers approaches

```               1
Φ = 1 + ---------------
1
1 + -----------
1
1 + -------
1
1 + ---
1 + ...
```

...or, expressed more compactly using limits:

```Φ = lim fn+1/fn
n→∞
```

The logarithmic spiral is not limited to non-human elements in nature. As a human embryo grows, its spine unfolds in a pattern very similar to the logarithmic spiral. This is not the only place the Golden Ratio appears in the human body, however. Leonardo da Vinci, Renaissance man that he was, noticed this and used it in his art. The well-known Vitruvian Man employs the Golden Ratio extensively; for instance, the distances between the top of his head, the bottom of his feet, and his navel between them lie on a perfect Golden Section. The face of the Mona Lisa can be neatly inscribed in a Golden Rectangle, and the positions of her eyes, nose and mouth are also placed according to the Golden Ratio.

It is sometimes said that the "most aesthetically pleasing" human face and body relies entirely on the Golden Ratio, and that this is the reason it is so aesthetically satisfying in art and architecture as well.

This information is common mathematical knowledge, but my primary sources included:
The "Phi-Nest" (http://goldennumber.net)
The Golden Mean (http://galaxy.cau.edu/tsmith/KW/golden.html)

I saw a BBC documentary about the human face.

This episode was about beauty. There where a number of different theories about what makes a face 'perfect'/beautiful.

A doctor (plastic surgeon) had used the golden ratio (rounded: 1:1.618) to make a mask/map (a face made of points and lines on a piece of paper) of a human face using geometry with the golden ratio.

They took a sample of people who where considered beautiful, and the mask fitted better than other people that where considered not so beautiful.

The BBC program can be found here: http://www.bbc.co.uk/science/humanbody/humanface/beauty_grid.shtml

Also, this number, seems to pop-up in the movie pi.

How often have you been eating a meal in one of life's eating establishments, and thought, "I wish my napkin was more aesthetically sized."?

I thought so, which is why I bring you 5 easy steps to make your eating experience that little bit more perfect.

```          +-----------+
|           |
|           |
|           |
|           |
+-----------+```
• Divide the square in half.
```          +-----+-----+
|     |     |
|     |     |
|     |     |
|     |     |
+-----+-----+```
• Draw a diagonal across one of half of the square.
```          +-----+-----+
|     |   / |
|     |  /  |
|     | /   |
|     |/    |
+-----+-----+```
• Use the diagonal as the radius of a circle, and complete an arc to the baseline of the square.
```          +-----+-----+-
|     |   / |  \
|     |  /  |    \
|     | /   |     \
|     |/    |      |
+-----+-----+------+```
• Complete the rectangle from this point on the baseline.
```          +-----+-----+------+
|     |   / |  \   |
|     |  /  |    \ |
|     | /   |     \|
|     |/    |      |
+-----+-----+------+```
You now are the proud owner of a napkin that is a golden rectangle. What a pleasure wiping your mouth will be.

But, I hear you ask, how do you know that this is a golden rectangle? Well, dear reader, read on.

Lets say the original square was `x` by `x`. Given that, the length of the diagonal can be found using the school boy favourite, Pythagoras:

```           c2 = a2 + b2

x2
= -  + x2
4

__________
| x2
c   =  | -  + x2
\| 4

_____
| 5x2
c   =  | ---
\|  4

```
With that said, the bottom edge of the golden rectangle is:
```                 _____
x    | 5x2
- +  | ---
2   \|  4

_____
x + \| 5x2
-----------
2

x ( 1 + √5 )
-------------
2
```
So, if we now consider this in terms of the ratio of short to long edge we have:
```               x ( 1 + √5 )
x :  ------------
2

1 + √5
1 :  ------
2
```
Which, my fellow geometrist, is the golden ratio.
first 10,000 digits of the golden ratio:
```
1.61803 39887 49894 84820 45868 34365 63811 77203 09179 80576
28621 35448 62270 52604 62818 90244 97072 07204 18939 11374
84754 08807 53868 91752 12663 38622 23536 93179 31800 60766
72635 44333 89086 59593 95829 05638 32266 13199 28290 26788
06752 08766 89250 17116 96207 03222 10432 16269 54862 62963
13614 43814 97587 01220 34080 58879 54454 74924 61856 95364
86444 92410 44320 77134 49470 49565 84678 85098 74339 44221
25448 77066 47809 15884 60749 98871 24007 65217 05751 79788
34166 25624 94075 89069 70400 02812 10427 62177 11177 78053
15317 14101 17046 66599 14669 79873 17613 56006 70874 80710
13179 52368 94275 21948 43530 56783 00228 78569 97829 77834
78458 78228 91109 76250 03026 96156 17002 50464 33824 37764
86102 83831 26833 03724 29267 52631 16533 92473 16711 12115
88186 38513 31620 38400 52221 65791 28667 52946 54906 81131
71599 34323 59734 94985 09040 94762 13222 98101 72610 70596
11645 62990 98162 90555 20852 47903 52406 02017 27997 47175
34277 75927 78625 61943 20827 50513 12181 56285 51222 48093
94712 34145 17022 37358 05772 78616 00868 83829 52304 59264
78780 17889 92199 02707 76903 89532 19681 98615 14378 03149
97411 06926 08867 42962 26757 56052 31727 77520 35361 39362
10767 38937 64556 06060 59216 58946 67595 51900 40055 59089
50229 53094 23124 82355 21221 24154 44006 47034 05657 34797
66397 23949 49946 58457 88730 39623 09037 50339 93856 21024
23690 25138 68041 45779 95698 12244 57471 78034 17312 64532
20416 39723 21340 44449 48730 23154 17676 89375 21030 68737
88034 41700 93954 40962 79558 98678 72320 95124 26893 55730
97045 09595 68440 17555 19881 92180 20640 52905 51893 49475
92600 73485 22821 01088 19464 45442 22318 89131 92946 89622
00230 14437 70269 92300 78030 85261 18075 45192 88770 50210
96842 49362 71359 25187 60777 88466 58361 50238 91349 33331
22310 53392 32136 24319 26372 89106 70503 39928 22652 63556
20902 97986 42472 75977 25655 08615 48754 35748 26471 81414
51270 00602 38901 62077 73224 49943 53088 99909 50168 03281
12194 32048 19643 87675 86331 47985 71911 39781 53978 07476
15077 22117 50826 94586 39320 45652 09896 98555 67814 10696
83728 84058 74610 33781 05444 39094 36835 83581 38113 11689
93855 57697 54841 49144 53415 09129 54070 05019 47754 86163
07542 26417 29394 68036 73198 05861 83391 83285 99130 39607
20144 55950 44977 92120 76124 78564 59161 60837 05949 87860
06970 18940 98864 00764 43617 09334 17270 91914 33650 13715
76601 14803 81430 62623 80514 32117 34815 10055 90134 56101
18007 90506 38142 15270 93085 88092 87570 34505 07808 14545
88199 06336 12982 79814 11745 33927 31208 09289 72792 22132
98064 29468 78242 74874 01745 05540 67787 57083 23731 09759
15117 76297 84432 84747 90817 65180 97787 26841 61176 32503
86121 12914 36834 37670 23503 71116 33072 58698 83258 71033
63222 38109 80901 21101 98991 76841 49175 12331 34015 27338
43837 23450 09347 86049 79294 59915 82201 25810 45982 30925
52872 12413 70436 14910 20547 18554 96118 08764 26576 51106
05458 81475 60443 17847 98584 53973 12863 01625 44876 11485
20217 06440 41116 60766 95059 77578 32570 39511 08782 30827
10647 89390 21115 69103 92768 38453 86333 32156 58296 59773
10343 60323 22545 74363 72041 24406 40888 26737 58433 95367
95931 23221 34373 20995 74988 94699 56564 73600 72959 99839
12881 03197 42631 25179 71414 32012 31127 95518 94778 17269
14158 91177 99195 64812 55800 18455 06563 29528 59859 10009
08621 80297 75637 89259 99164 99464 28193 02229 35523 46674
75932 69516 54214 02109 13630 18194 72270 78901 22087 28736
17073 48649 99815 62554 72811 37347 98716 56952 74890 08144
38405 32748 37813 78246 69174 44229 63491 47081 57007 35254
57070 89772 67546 93438 22619 54686 15331 20953 35792 38014
60927 35102 10119 19021 83606 75097 30895 75289 57746 81422
95433 94385 49315 53396 30380 72916 91758 46101 46099 50550
64803 67930 41472 36572 03986 00735 50760 90231 73125 01613
20484 35836 48177 04848 18109 91602 44252 32716 72190 18933
45963 78608 78752 87017 39359 30301 33590 11237 10239 17126
59047 02634 94028 30766 87674 36386 51327 10628 03231 74069
31733 44823 43564 53185 05813 53108 54973 33507 59966 77871
24490 58363 67541 32890 86240 63245 63953 57212 52426 11702
78028 65604 32349 42837 30172 55744 05837 27826 79960 31739
36401 32876 27701 24367 98311 44643 69476 70531 27249 24104
71670 01382 47831 28656 50649 34341 80390 04101 78053 39505
87724 58665 57552 29391 58239 70841 77298 33728 23115 25692
60929 95942 24000 05606 26678 67435 79239 72454 08481 76519
73436 26526 89448 88552 72027 47787 47335 98353 67277 61407
59171 20513 26934 48375 29916 49980 93602 46178 44267 57277
67900 19191 90703 80522 04612 32482 39132 61043 27191 68451
23060 23627 89354 54324 61769 97575 36890 41763 65025 47851
38246 31465 83363 83376 02357 78992 67298 86321 61858 39590
36399 81838 45827 64491 24598 09370 43055 55961 37973 43261
34830 49494 96868 10895 35696 34828 17812 88625 36460 84203
39465 38194 41945 71426 66823 71839 49183 23709 08574 85026
65680 39897 44066 21053 60306 40026 08171 12665 99541 99368
73160 94572 28881 09207 78822 77203 63668 44815 32561 72841
17690 97926 66655 22384 68831 13718 52991 92163 19052 01568
63122 28207 15599 87646 84235 52059 28537 17578 07656 05036
77313 09751 91223 97388 72246 82580 57159 74457 40484 29878
07352 21598 42667 66257 80770 62019 43040 05425 50158 31250
30175 34094 11719 10192 98903 84472 50332 98802 45014 36796
84416 94795 95453 04591 03138 11621 87045 67997 86636 61746
05957 00034 45970 11352 51813 46006 56553 52034 78881 17414
99412 74826 41521 35567 76394 03907 10387 08818 23380 68033
50038 04680 01748 08220 59109 68442 02644 64021 87705 34010
03180 28816 64415 30913 93948 15640 31928 22785 48241 45105
03188 82518 99700 74862 28794 21558 95742 82021 66570 62188
09057 80880 50324 67699 12972 87210 38707 36974 06435 66745
89202 58656 57397 85608 59566 53410 70359 97832 04463 36346
48548 94976 63885 35104 55272 98242 29069 98488 53696 82804
64597 45762 65143 43590 50938 32124 37433 33870 51665 71490
05907 10567 02488 79858 04371 81512 61004 40381 48804 07252
44061 64290 22478 22715 27241 12085 06578 88387 12493 63510
68063 65166 74322 23277 67755 79739 92703 76231 91470 47323
95512 06070 55039 92088 44260 37087 90843 33426 18384 13597
07816 48295 53714 32196 11895 03797 71463 00075 55975 37957
03552 27144 93191 32172 55644 01283 09180 50450 08992 18705
12118 60693 35731 53895 93507 90300 73672 70233 14165 32042
34015 53741 44268 71540 55116 47961 14332 30248 54404 09406
91145 61398 73026 03951 82816 80344 82525 43267 38575 90056
04320 24537 27192 91248 64581 33344 16985 29939 13574 78698
95798 64394 98023 04711 69671 57362 28391 20181 27312 91658
99527 59919 22031 83723 56827 27938 56373 31265 47998 59124
63275 03006 05925 67454 97943 50881 19295 05685 49325 93553
18729 14180 11364 12187 47075 26281 06869 83013 57605 24719
44559 32195 53596 10452 83031 48839 11769 30119 65858 34314
42489 48985 65584 25083 41094 29502 77197 58335 22442 91257
36493 80754 17113 73924 37601 43506 82987 84932 71299 75122
86881 96049 83577 51587 71780 41069 71319 66753 47719 47922
63651 90163 39771 28473 90793 36111 19140 89983 05603 36106
09871 71783 05543 54035 60895 29290 81846 41437 13929 43781
35604 82038 94791 25745 07707 55751 03002 42072 66290 01809
04229 34249 42590 60666 14133 22872 26980 69014 59945 11995
47801 63991 51412 61252 57282 80664 33126 16574 69388 19510
64421 67387 18000 11004 21848 30258 09165 43383 74923 64118
38885 64685 14315 00637 31904 29514 81469 42431 46089 52547
07203 74055 66913 06922 09908 04819 45297 51106 50464 28105
41775 52590 95187 13188 83591 47659 96041 31796 02094 15308
58553 32387 72538 02327 27632 97737 21431 27968 21671 62344
21183 20180 28814 12747 44316 88472 18459 39278 14354 74099
99907 22332 03059 26297 66112 38327 98331 69882 53931 26200
65037 02884 47828 66694 04473 07947 10476 12558 65837 52986
23625 09998 23233 59715 50723 38383 32440 81525 77819 33642
62630 43302 65895 81708 00451 27887 31159 35587 74721 72564
94700 05163 66725 77153 92098 40950 32745 11215 36873 00912
19962 95227 65913 16370 93968 60727 13426 92623 15475 33043
79933 16581 10736 96431 42171 97943 40563 91551 21081 08136
26268 88569 74806 80601 16918 94175 02722 98741 58699 17914
53499 46244 41940 12197 85860 13736 60828 69072 23651 47713
91268 74209 66513 78756 20591 85432 88883 41742 92090 15631
33283 19357 56220 89713 76563 09785 01563 15498 24564 45865
42479 29357 22828 75060 84814 53351 35218 17295 87932 99117
10032 47622 20521 94645 10536 24505 12988 43087 13444 39507
24426 73514 62861 79918 32336 45983 69637 63272 25756 91597
23954 38305 20866 47474 23815 11079 27349 48369 52396 47926
89936 98324 91799 95027 89500 06045 96613 13463 36302 49499
51480 80532 90179 02975 18251 58750 49007 43518 79835 11836
03272 27726 01717 40453 55716 58855 57829 72910 61958 19351
71055 48257 93070 91005 76358 69901 92972 17995 16873 11755
63144 48564 81002 20014 25454 05542 92734 58837 11602 09947
94572 08237 80436 87189 44805 63689 18258 02444 99631 87834
20274 91015 33579 10727 33625 32890 69334 74123 80222 20116
26277 11930 85448 50295 41913 20040 09998 65566 65177 56640
95365 61978 97818 38045 10303 56510 13158 94589 02871 86108
69058 93947 13680 14845 70018 36649 56472 03294 33437 42989
46427 41255 14359 05843 48409 19548 70152 36140 31739 13903
61644 01984 55051 04912 11697 92001 20199 96050 69949 66403
03508 63692 90394 10070 19450 53201 62348 72763 23273 24494
39630 48089 05542 51379 72331 47518 52070 91025 06368 59816
79530 48181 00739 42453 17002 38804 75983 43234 50414 25843
14063 61272 10960 22824 23378 22809 02797 65960 77710 84939
15174 88731 68777 13522 39009 11711 73509 18600 65462 00990
24975 85277 92542 78165 97038 34950 58010 62615 53336 91093
78465 97710 52975 02231 73074 12177 83441 89411 84596 58610
29801 87787 42744 56386 69661 27724 50384 58605 26415 10304
08982 57777 54474 11533 20764 07588 16775 14975 53804 71162
96677 71005 87664 61595 49677 69270 54962 39398 57092 55070
27406 99781 40843 12496 53630 71866 53371 80605 87422 42598
16530 70525 73834 54157 70542 92162 99811 49175 08611 31176
57731 72095 61565 64786 95474 48927 13206 08063 54577 94624
14531 06698 37421 13798 16896 38235 33304 47788 31693 39728
72891 81036 64083 26985 69882 54438 51667 58622 89930 69643
46848 97514 84087 90396 47604 20361 02060 21717 39447 02634
87633 65439 31952 29077 38361 67389 81178 12424 83655 78105
03416 94515 63626 04300 36657 43108 47665 48777 80128 57792
36454 18522 44723 61713 74229 25584 15931 35612 86637 16703
28072 17155 33926 46325 73067 30639 10854 10886 80857 42838
58828 06023 03341 40855 03909 73538 72613 45119 62926 41599
52127 89311 35443 14601 52730 90255 38271 04325 96622 67439
03745 56361 22861 39078 31943 35705 90038 14870 08986 61315
39819 58574 42330 44197 08566 96722 29314 27307 41384 88278
89755 88860 79973 87044 70203 16683 48569 41990 96548 02982
49319 81765 79268 29855 62972 30106 82777 23516 27407 83807
43187 78273 18211 91969 52800 51608 79157 21288 26337 96823
12725 62870 00150 01829 29757 72999 35790 94919 64076 34428
61575 71354 44278 98383 04045 47027 10194 58004 25820 21202
34458 06303 45033 65814 72185 49203 67998 99729 35353 91968
12133 19516 53797 45399 11149 42444 51830 33858 84129 04018
17818 82137 60066 59284 94136 77543 17451 60540 93871 10368
71521 16404 05821 93447 12044 82775 96054 16948 64539 87832
62695 48013 91501 90389 95931 30670 31866 16706 63719 64025
69286 71388 71466 31189 19268 56826 91995 27645 79977 18278
75946 09616 17218 86810 94546 51578 86912 24106 09814 19726
86192 55478 78992 63153 59472 92282 50805 42516 90681 40107
81796 02188 53307 62305 56381 63164 01922 45450 32576 56739
25997 65175 30801 42716 07143 08718 86285 98360 37465 05713
42046 70083 43275 42302 77047 79331 11836 66903 23288 53068
73879 90713 59007 40304 90745 98895 13647 68760 86784 43238
24821 89306 17570 31956 38032 30819 71936 35672 74196 43872
62587 06154 33072 96370 38127 51517 04060 05057 59488 27238
56345 15639 05265 77104 26459 47604 05569 50959 84088 89037
62079 95663 88017 86185 59159 44111 72509 23132 79771 13803
```

[Editor's note, 12/29/2005: added <small> tags.

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