The largest equilateral triangle

This device cannot show the 3D view. Follow the step pictures and text below instead.

1. 

   1. Crease the centre line

   White side up. Fold the left edge to the right edge and unfold to make a vertical centre line.

2. 

   2. Corner onto the centre line (60°)

   Fold the bottom-right corner up onto the centre line, with the crease starting exactly at the bottom-left corner. The folded edge now makes 60° with the bottom.

3. 

   3. Halve the left angle (75°)

   Fold the left edge down to lie exactly along the folded edge, again creasing from the bottom-left corner. This halves the 30° that was left.

4. 

   4. Unfold the bottom corner

   Unfold only the bottom corner from step 2. Leave the top-left part folded.

5. 

   5. Halve the bottom angle (15°)

   Fold the bottom edge up onto the crease from step 2, creasing from the bottom-left corner. The two new fold lines are now exactly 60° apart.

6. 

   6. Fold the last corner

   Fold the top-right corner down through all layers along the line joining the two points where the folds meet the top and right edges.

7. 

   7. Turn over: done

   Turn it over: the largest equilateral triangle you can fold from the square. Measure the three sides and compare!