There are a total of 12 angles formed at the center. Dividing 360 degrees equally among them gives 30 degrees per angle and splits the paper into 12 triangles. Our focus will be on any one of the larger right triangles formed in this way.
Without loss of generality, let the short side of this triangle be equal to 1. Then by 30-60-90 triangle properties, the long side is \( \sqrt{3} \). This triangle is similar to the triangle which has the entire sheet of paper's length and width as legs, so by similarity, the entire sheet of paper has its short/long side in the ratio \( 1 / \sqrt{3} \) .