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Old May 16th, 2011, 04:54 AM   #21981
toren1776
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What? Math is not allowed on this forum? I was not aware of this fact.
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Old May 16th, 2011, 08:03 AM   #21982
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Here's 2 Videos my friend took on the 12th....



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Old May 16th, 2011, 02:30 PM   #21983
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Quote:
Originally Posted by toren1776 View Post
What? Math is not allowed on this forum? I was not aware of this fact.
I think it's great that you took the time to work it out. No doubt the architects and engineers had to use substantial amounts of mathematics to design this building, so it is hardly off-topic. So we are around 5 or 6 floors from this perfect octagon now?
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Old May 16th, 2011, 05:10 PM   #21984
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How Vissible the tower was earlier today:

By Vivalabamdude on Imageshack
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Old May 16th, 2011, 05:54 PM   #21985
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Old May 16th, 2011, 06:43 PM   #21986
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cant see anything, thats on morning time?
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Old May 16th, 2011, 07:07 PM   #21987
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Yep 7 am
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Old May 16th, 2011, 08:41 PM   #21988
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Quote:
Originally Posted by earthbuilder View Post
How Vissible the tower was earlier today:

By Vivalabamdude on Imageshack
Wow, kinda reminds me of September 10th, 2001. I was in 7th grade and it was a really rainy and shitty afternoon in the city with a lot of fog. We were able to look straight downtown at the Twin Towers from some of our classroom windows, about 2 miles uptown or so. It was so foggy that the twins were completely masked by fog. And I remember telling my mom when I got home that day "the twin towers totally disappeared!"
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Old May 16th, 2011, 09:18 PM   #21989
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image hosted on flickr

2011-03-02 37 by in.formed, on Flickr
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Old May 16th, 2011, 10:20 PM   #21990
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Quote:
Originally Posted by toren1776 View Post
Today I did a little mathematical exercise and was able to prove that the "octagon" is indeed on the 72nd floor. It took me some time to come up with, but in the end I figured out the height of the tower at which this "octagon" is found, which was 878 feet, and just about on the 72nd floor. To actually get the 878 figure, I used some pretty difficult triangle ratio methods and eventually mashed out this formula:

o=(ah/(a+b))+185

o=the height at which the octagon is found (the variable)
h=height of any one of 1WTC's triangular facades=1,183 feet
a=half of the base of any of the four larger triangle facades=100 feet
b=half of the base of any of the four smaller triangle facades=70.7107 feet
height of base=185 feet

Proving this formula would be impossible on this forum given that it is largely a geometrical proof and requires multiple diagrams to be drawn. The most important thing to know is that the facade triangles don't all have the same area (4 are larger, 4 are smaller) and therefore the octagon is a little higher up than just at the midpoint of the facade triangle height.

Also, does anyone know who first came up with the 72nd floor as the "octagon floor" that everyone keeps mentioning?
That just simplifies to o = (2-√2)h + 185
So the base measurements are irrelevant, which makes sense if you think about it.
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Old May 16th, 2011, 10:34 PM   #21991
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Quote:
Originally Posted by toren1776 View Post
Today I did a little mathematical exercise and was able to prove that the "octagon" is indeed on the 72nd floor. It took me some time to come up with, but in the end I figured out the height of the tower at which this "octagon" is found, which was 878 feet, and just about on the 72nd floor. To actually get the 878 figure, I used some pretty difficult triangle ratio methods and eventually mashed out this formula:

o=(ah/(a+b))+185

o=the height at which the octagon is found (the variable)
h=height of any one of 1WTC's triangular facades=1,183 feet
a=half of the base of any of the four larger triangle facades=100 feet
b=half of the base of any of the four smaller triangle facades=70.7107 feet
height of base=185 feet

Proving this formula would be impossible on this forum given that it is largely a geometrical proof and requires multiple diagrams to be drawn. The most important thing to know is that the facade triangles don't all have the same area (4 are larger, 4 are smaller) and therefore the octagon is a little higher up than just at the midpoint of the facade triangle height.

Also, does anyone know who first came up with the 72nd floor as the "octagon floor" that everyone keeps mentioning?
Great stuff..

Zen was the man..He knew everything..
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Old May 16th, 2011, 11:08 PM   #21992
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image hosted on flickr

Look how quick the Freedom Tower us going up. by TomBudd, on Flickr
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Old May 17th, 2011, 02:49 AM   #21993
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can someone answer my question again...does this building taper inwards towards the core at all four (or eight) facades?
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Old May 17th, 2011, 02:50 AM   #21994
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Quote:
Originally Posted by spiller9 View Post
can someone answer my question again...does this building taper inwards towards the core at all four (or eight) facades?
I think four sides only. If they all do, it would end up basically a pyramid.
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Old May 17th, 2011, 03:32 AM   #21995
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Quote:
That just simplifies to o = (2-√2)h + 185
So the base measurements are irrelevant, which makes sense if you think about it.
Wow, thanks, that was pretty ingenious. It's not that easy to simplify, but I see how you got there. So yes, the final formula is o=(2-√2)h + 185 where h is the height of any triangle facade (1,183 feet) and o is the height at which the regular octagon is found (878 feet). I like how math makes everything simple and elegant.

Last edited by toren1776; May 17th, 2011 at 04:08 AM.
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Old May 17th, 2011, 03:53 AM   #21996
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http://featuresblogs.chicagotribune....e-center-.html
According to the NYTimes and the Chicago Tribune, the prismatic glass for the base of the tower is not working out and they have sent architects back to find a new solution
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Old May 17th, 2011, 04:19 AM   #21997
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^Previeous pages

image hosted on flickr

ground zero by Bébé Poubelle, on Flickr

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Lower Manhattan from above by Plaid Ninja, on Flickr
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Old May 17th, 2011, 04:27 AM   #21998
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Flying in a helicopter over NYC by benjamin running, on Flickr
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Old May 17th, 2011, 05:57 AM   #21999
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As you all guessed, the middle of a triangular face of this building doesn't mean that in that elevation is where the perfect octagon should be. In fact, there's a variation between the height of a completely vertical triangular face (N,S,E,W) and a diagonal triangular face(NE,NW,SE,SW).
Not good explaining, but a diagram should give you an idea why 72nd floor is the perfect octagon (structurally):



Triangles are such interesting shapes...
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Old May 17th, 2011, 07:27 PM   #22000
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Quote:
Not good explaining, but a diagram should give you an idea why 72nd floor is the perfect octagon (structurally):
Nice work Otie. Here is another way you could look at it (did this in 10 minutes so not of the best quality):

[IMG][/IMG]

Last edited by toren1776; May 18th, 2011 at 03:05 PM.
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