What paper went into that flap?

How would you make a single flap?

We're going to learn how to make one flap.

Well, there are other ways of making a flap.

I didn't have to try to flap my wings.

So that's the flap, and all the rest of the paper's left over.

It's very complicated, but it turns out they flap their wings very quickly.

And if I make the flap from the middle, it uses a full circle.

If I put the flap on the edge, it uses a half circle of paper.

And you can see there, it needs a quarter circle of paper to make a flap.

So, no matter how I make a flap, it needs some part of a circular region of paper.

This issue continues to hinge on the training of some 600 security auxiliaries drawn from within the ranks of the FN.

If I make the flap as skinny as possible, I get to the limit of the minimum amount of paper needed.

The technical questions are complex, and the proverbial devil really is in the countless details. But prospects for a deal will hinge on resolving three broad issues.

The U.N. you know, they took 20 years just to add a flap to a tent, but I think we have some more exciting things.

Attainment of the MDGs would largely hinge on how the productive sector was harnessed to enable it to generate the resources necessary to achieve the goals in question.

It is generally believed and there is a modicum of truth in it that success in nuclear disarmament does not hinge on technical issues, but is a matter of political will.

And from that stick figure, I somehow have to get to a folded shape that has a part for every bit of the subject, a flap for every leg.

And we tackle this problem by building giant, dynamically scaled model robot insects that would flap in giant pools of mineral oil where we could study the aerodynamic forces.

Well, if I unfold it and go back to the crease pattern, you can see that the upper left corner of that shape is the paper that went into the flap.

Take a square. Fold it in half, fold it in half, fold it again, until it gets long and narrow, and then we'll say at the end of that, that's a flap.

The EU must make it clear that it is ready to support Serbia and the region as a whole in realizing its European aspirations. European security is hinged on Serbian integration, just as Serbian aspirations hinge on the EU.

We have a long way to go, probably in a climate that will not turn favorable to immigration for many years. How much progress we can make will hinge on our ability to break through the myths about migration.

But, while the French election s outcome will hinge to a crucial extent on European crisis politics, Germany s government acts as if this were none of its concern. Instead, the main almost exclusive topic in Berlin is the upcoming election.

There are some larger regional consequences in all of this. The Association of Southeast Asian Nations (ASEAN) has tenaciously fought for its place as the geopolitical hinge between East and South Asia, and an important player in Asia Pacific economic and security diplomacy.

If the Round is to be completed by 2006, which is widely recognized as the only narrow window available, further progress will now hinge on the outcome of the 6th WTO Ministerial Conference, to be held in Hong Kong, China, in December 2005.

The possible existence of the organization's responsibility appears to hinge on whether the organization's binding decision actually requires the wrongful act to be done, or whether the act is just one of the ways that a member State may select when implementing the decision.

That said, the economic outlook can never be fully analyzed with conventional statistical models, for it may hinge on something that such models do not include our finding some way to replace one narrative currently a tale of out of control debt with a more inspiring story.

Unless emerging market governments take advantage of the limited space provided by their foreign exchange reserves and floating currencies to enact vital structural reforms, the onus of adjustment will fall on interest rates, compounding the effects of slowing growth and the risks associated with bad debt. Whether this becomes a systemic issue affecting the entire global economy will hinge on China.

But attached to the base of the wing is a set of little, tiny control muscles that are not very powerful at all, but they're very fast, and they're able to reconfigure the hinge of the wing on a stroke by stroke basis, and this is what enables the fly to change its wing and generate the changes in aerodynamic forces which change its flight trajectory.

And it turns out that the insects flap their wings in a very clever way, at a very high angle of attack that creates a structure at the leading edge of the wing, a little tornado like structure called a leading edge vortex, and it's that vortex that actually enables the wings to make enough force for the animal to stay in the air.

PRINCETON Forty years ago, I stood with a few other students in a busy Oxford street handing out leaflets protesting the use of battery cages to hold hens. Most of those who took the leaflets did not know that their eggs came from hens kept in cages so small that even one bird the cages normally housed four would be unable to fully stretch and flap her wings.