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There are certain buildings and places on this planet where mathematicians can find delight because of the history, the art, the architecture, and for other reasons. For example, the Alhambra with it's heavy use of geometric patterns. Or, perhaps, going to the leaning tower of Pisa and playing games with calculating where it's shadow will be cast. Clearly, there are many places with historical or related significance to those interested in mathematics. I would enjoy hearing about some from people here -- in particular, I would love to hear about any places in the middle east.

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I dont know about the middle East but would Jantar Mantar in India interest you? –  Shahab Jan 5 '12 at 2:25
    
lonelyplanet.com/thorntree/thread.jspa?threadID=2074113 seems to have a similar discussion –  Bhargav Jan 5 '12 at 2:36
    
Thales also used geometry to calculate height of pyramids in Egypt. In general here's wikipedia's entry on Mathematics and Architecture which discusses usage of fractals in Hindu temples. –  Sniper Clown Jan 5 '12 at 2:46
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Migrate to Travel.SE? –  Nate Eldredge Jan 5 '12 at 5:04
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I vote against closing this thread: if there was room for "a book every mathematician should read" then I think there's room for "a place every mathematician should visit"... In any case: it was suggested to migrate to travel.SE: is there a significant user base on travel.SE having the mathematical background to answer this question non-trivially? –  t.b. Jan 7 '12 at 2:29

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For sake of pure history associated with Göttingen it should be a Mecca for any mathematicians. I also remember once my Calculus professor talk about an auditorium for acoustics where if you whisper at one end and if your friend is standing at the foci, then she can hear you. (This blog discusses it a bit.)

As far as architecture inspired by mathematics:

However, the go-to-guide would be Jane Burry's The New Mathematics of Architecture (Google images of some of its content)

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See the Mathematical Tourist column, by Ivars Peterson, at the MAA site, for a large number of suggestions.

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