ABSTRACT
Try to do the following without drawing or writing anything, think for several minutes about the problem then reflect on what was going on in your mind when you were thinking about it. You may find it helpful to close your eyes after you have read it:
Unless your mind was totally inactive, or full of thoughts unrelated to the problem, then what you have been engaged in is mental mathematics and metacognition (thinking about your own thinking). It could be that you were able to visualise a quadrilateral mentally and circumscribe a circle and to ‘see’ them in your head sufficiently vividly to be able to answer the initial question. Many people do not have clear ‘pictures in the head’; you may have been bringing to mind memories of diagrams you had drawn or had seen. You may instead (or as well as) have been trying to recall any circle theorems that might help or trying to remember if you had ever done anything like this before. Mixed up with these images and thoughts may well have been feelings of frustration and despondency if you were unsuccessful or a sense of euphoria if you enjoyed working on the problem.
