Make intricate geometric designs with thread on paper. I will show the steps to make a triangle here, but they work the same for other shapes.

Step 1: Materials

You will need:

Sewing things:
-thread
-3 needles
-a needle threader
-scissors

And also:
-a ruler
-sticky tape
-2 pieces of cardstock (I used index cards here)
-a pencil

And Either:
-a compass
or
-a protractor

Step 2: Design the Template

On the first piece of cardstock, draw a geometric figure. If you know how, it can be worthwhile to construct it with a compass and straightedge, if only because it makes the template look really cool when you're done. But it's just as easy to botch it with a ruler and maybe a protractor.

Once your figure is drawn, make evenly spaced tick-marks on each edge. If you use a compass and straightedge, this is done by bisecting each segment three or more times.

Step 3: Poke Holes

Poke holes at each tick mark on your template with a needle.

Then, I prefer to do this on the edge of a desk, put the template on top of the blank piece of cardstock. Poke two of the three needles into corners of the triangle so that the pieces cannot rotate, and then use the third needle to punch the remaining holes on that side through the bottom sheet. When you finish a side, move the needles to the next side and continue.

Step 4: The Outline

Thread an arm's length piece of thread and tape the other end to the back. Go around the outline of the triangle twice so that all sides have thread on them on both sides. When you get back to the beginning, untape the end and tie it in a loop.

(If you have an odd shape, it may take multiple pieces of thread and may not form a loop, but it's ok to just leave the ends taped as long as they're on the back.)

Step 5: The First Parabola

The simplest thing to curve stitch is a parabola.

Start by threading a two or three arm's-length piece of thread and taping the other end to the back. Go up through a corner and go back down through the hole on the opposite side closest to either opposite corner. Come back up through the hole two away from that corner and then cross back over to a hole one away from the first corner.

The more holes you have, the closer this will approximate a parabola.

Step 6: The Second Parabola

When the first parabola is finished, the thread should be coming out a corner onto the front side. Begin a second parabola in the same way you began the first, except with all the corners and sides rotated. You should find yourself overlapping on the bottom on one side of the triangle, but not on the other.

Step 7: The Third Parabola and Finishing Up

From the second parabola continue the third in the same way as the first and second. When you reach the end, and if everything came out evenly, you can tie off the ends again, making it neatly self-contained. But again, tape on the back isn't a big deal, and could be necessary.