Shortest triangle strip knot Join rigid equilateral triangles at the edges to make a strip of rectangles.  What is the minimal number of triangles needed to make a knot?  The triangles should not intersect.  
Same question -- are fewer triangles needed if only the free edge/edges needs to be knotted/linked?  
Same question, but with a strip of congruent triangles instead.
 A: So first, I made some strips of paper, that were .875=7/8th inch by 11in.  This is to get close to the width being $\frac{\sqrt{3}}{2}\approx.866$in which is the height of an equilateral triangle with edge length 1.  Then make a mark at 1 inch on one long side of the paper and on the other side make a mark at 1/2 inch.  Fold a straight line between the two marks and this is the first edge of your triangles. Then lay that edge along the edge you made the 1/2 inch mark to make a full equilateral triangle and crease the fold. Continue folding to make a strip of equilateral triangles.  I cut my strip off at 16 full triangles, but really we only need 15, but we will overlap the last one with the first.

Now, grab it by the 8th triangle as in the picture below. Make sure the first triangle points toward you and the one you are holding is pointing away. 

Take the first triangle and lay it under the 8th triangle you are holding. Note that there are many ways you can lay these two triangles together. Bend the first triangle around like we were going to role the paper up. The way we want hold them will form a hole that is a triangle also.

Okay, now we have the tail sticking out away from us, we bend it back and put it behind and pull it out through the triangle hole we made.  If you are holding it like me, the tail will go in where your index finger is and out the triangle hole, the direction your index is pointing.

Now, you should start to really see that we have 5 triangles meeting on top of this shape, with a single triangle hole still where we just passed the last piece through.  There is also a five triangles meeting on the bottom.  Now we are almost done.  Lay the tail over the front to cover the triangle hole.  You will have to lift your thumb and but the second to last triangle over your triangle your thumb was on.  Hold it again with your thumb and you should have just one triangle sticking out.

Finally, fold your one remaining tail triangle up inside of the shape where your index finger was.  Done!  Here it is without my thumb(finally) from the same view.  

And the bottom view, where we still have one hole.

Anyway, I hope that was at least reasonable to follow... I know describing origami moves is hard and I am not very good at it.  Let me know if you have questions.  This is not a proof that this is the minimum number of triangles, but honestly I would be surprised at this point if it can be done with less.
