TITLE: What would you want to see at the Museum of Mathematics?
QUESTION [112 upvotes]: EDIT (30 Nov 2012): MoMath is opening in a couple of weeks, so this seems like it might be a good time for any last-minute additions to this question before I vote to close my own question as "no longer relevant".

As some of you may already know, there are plans in the making for a Museum of Mathematics in New York City.  Some of you may have already seen the Math Midway, a preview of the coming attractions at MoMath.
I've been involved in a small way, having an account at the Math Factory where I have made some suggestions for exhibits.  It occurred to me that it would be a good idea to solicit exhibit ideas from a wider community of mathematicians.

What would you like to see at MoMath?

There are already a lot of suggestions at the above Math Factory site; however, you need an account to view the details.  But never mind that; you should not hesitate to suggest something here even if you suspect that it has already been suggested by someone at the Math Factory, because part of the value of MO is that the voting system allows us to estimate the level of enthusiasm for various ideas.
Let me also mention that exhibit ideas showing the connections between mathematics and other fields are particularly welcome, particularly if the connection is not well-known or obvious.

A couple of the answers are announcements which may be better seen if they are included in the question.
Maria Droujkova: We are going to host an open online event with Cindy Lawrence, one of the organizers of MoMath, in the Math Future series. On January 12th 2011, at 9:30pm ET, follow this link to join the live session using Elluminate. 
George Hart: ...we at MoMath are looking for all kinds of input. If you’re at the Joint Math Meetings this week, come to our booth in the exhibit hall to meet us, learn more, and give us your ideas.

REPLY [21 votes]: https://www.scribd.com/document/479581247/Letter-to-MoMath-Board
Update: many of us got together to take a stand against unethical practices at the museum. See the above open letter to the Board of Trustees which recommends the replacement of the CEO Cindy Lawrence.
The concerns raised therein are at the intersection of the problems observed by the cosigners and are not comprehensive.

After serving as Chief of Mathematics at MoMath for the better part of 2 years, I'd like to shed some new light on this.
Firstly, this thread was a beautiful idea, to prompt the community for ideas before the Museum opened. However, at this point, the reality is: the last thing the Museum needs is more math ideas. What they need is proper implementation, and support for education. There is just a huge amount of work that one must do to get from a concept in a mathematician's brain to an interactive exhibit/lesson/activity that will work with kids. That is an ambitious thing to take on even if you don't have any other problems ... which the Museum does (see, for instance, the long history of complaints on Glassdoor -- they are a bit emotional, but having been there, I can say the complaints are well founded). I feel I did some great work there that I'm very proud of, but it was an uphill battle.
So here's what I'd like to see at the Museum:

proper administrative support for the existing ideas to be correctly
implemented,
a positive change in leadership so that the employees
will be treated with respect, and
for the Board of trustees to take seriously the education standards there should be for a place bearing the name "National Museum of Mathematics."