Thinking outside the box
The nine-point problem is a task in the field of practical problem solving in the psychology of thinking. The task is to connect 9 dots arranged in a square with a pen by four or four or less straight lines without lifting the pen. The problem was defined in 1963 by M. Scheerer.
In experiments, the approach of test subjects was investigated in this problem. Subjects that solve this task, often take a long time until they reach a solution to the problem. This is because people often tend to additional restrictions in solving problems to make. For example, subjects often try not to leave the square when drawing the lines. Scheerer takes the form of laws approach as an explanatory model.
If you also will not perceive the elements of the task as elements of Euclidean geometry, even solutions with less than four strokes up to one- line solutions are possible. For example, a solution in which a pen is selected, the line width is at least as large as the distance of the corner points, each forming an edge of the square formed by the points. Also, solutions that have something to do with spatial notion given. An example is that one cylindrical sets up the paper and then just about runs with the pin and the connecting points so. You lay the paper back towards normal, we see three parallel lines that are not perpendicular to the sheet edge. Children find such solutions often without major problems because they experience the points as small circles or lines with a line width. Only when this restriction is abandoned, a solution to the problem is possible by drawing on the square beyond. The nine-point problem is thus a good example for the English term thinking outside the box (in German about: outside the given framework think ) or the commonly used in German about looking outside the box, which plays an important role in the area of problem solving.