A simple method of making regular plane geometric figures from a square, a circle, or any regular or irregular geometric plane figure, by means of folding in such a manner that one clip of the scissors will give the desired result.

Principles Underlying The Work

THE principle upon which this folding is made is the division of the 3600 of the circle, or imaginary circle, contained within the enclosing plane figure into as many parts as there are sides or angles to the figure.

The paper may be square, circular, or of any regular or irregular shape.

We fold it into two equal parts, as in the circle (or as near equal as can be obtained in the other figure); this gives the 1800 fold.

By bisecting and folding, we get the 90° fold.

By dividing the 1800 fold into two and a half parts, and folding, we get the 720 fold.

By trisecting the 1800 fold, and folding, we get the 60° fold.

By dividing the 1800 fold into three and a half parts, and folding, we get the 51 3/7° fold.

By bisecting the 900 fold, and folding, we get the 450 fold.

By dividing the 180° fold into four and a half parts, and folding, we get the 400 fold.

By cutting each of these folds so that the result will be an isosceles triangle, we get from the 900 fold the square; from the J2° fold, the pentagon; from the 60° fold, the hexagon; from the 51 3/7° fold, the heptagon; from the 450 fold, the octagon; and from the 400 fold, the nonagon.

For the equilateral triangle it is necessary to cut the 6o° fold so that the result will be a right-angled triangle.

The accuracy of the result of this construction will naturally depend upon the accuracy of the folding and cutting.