How to draw a circle and a dot in the center without lifting your pencil

The circle and dot in the center is one of the oldest mathematical problems, the solution of which is essentially for many Buddhist enlightenment sort of cotton one hand. The reason of this task is to teach the subject to break away from the framework of standard thinking in strictly specified directories and to force to think in more than two axes of the coordinate system.

You will need

• pencil;
• - a sheet of paper.

Instruction

1. Carefully review the terms of the task assigned to you. Note the points about the drawing surface, the possibility of changing the surface and work in two-dimensional space. If a task has such a clause (e.g., "draw a circle and put a dot, using only two-dimensional space"), such a problem has no solution.
2. Take a sheet of loose paper. It is necessary, that it could well be bent, retaining traces of folds. Using a pencil, draw on paper a circle so that its edges almost touch the edge of the sheet. Since the task does not require strict adherence to geometric shapes, the circle may not be perfect. It is worth remembering that after the beginning of the tracings of the circle to tear the pencil from the paper impossible.
3. Fold the paper so that it touched the opposite edge, and repeat the operation. It is worth Recalling that tear the pencil from the line of the circle is impossible. Bend the sheet in the opposite to the pattern side out. In the end, a drawn circle and the crease line sheet form some semblance of a target – a circle and divide it into four equal parts cross.
4. Finally, fold the paper so that the edge of the circle with recorded with a pencil touched the center of the cross – points of intersection of bend lines. The problem is solved: the point in the center of the circle is set, and the pencil was torn from the circle and the whole worksheet. It should be noted that some teachers think this decision is invalid, in this case it is necessary to re-bend the leaf out and put the dot in the center of the circle using the puncture the surface of the sheet.