Figure 13

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Dinesh ^club

The meaning of active shaping holds not only for perception, but also especially for reflection and problem solving. I would like to use another example to illustrate the meaning of a hypothesis (or, as one might also say, a pre-judice) about a situation. If I set the reader the task of dividing a quadrilateral with a straight line into three triangles, many would at first deem this impossible. For if one draws a quadrilaterals, and then tries to obtain triangles by connecting opposite corners, one can obtain only two triangles, be the quadrilateral a square, a rectangle, a trapezoid, or a parallelogram.

It seems initially impossible to solve this problem. The impossibility, however, rests entirely on the hypothesis, or the prejudice as to what a quadrilateral ought to look like. If we restructure the task, striking off on an intellectual byway through active and creative reflection, the puzzle becomes suddenly solveable. In Figure 13, the reader will see a quadrilateral, intersected by a straight line that does divide it into three triangles. … Page 68

5 years ago.

Dinesh ^club

5 years ago.

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Figure 13

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