Mathematics is an exact science of imagination and beauty! You don’t have to be numerate students or mathematicians to be interested in this. A simple example is drawing a trapezoid ABCD (AB // CD):
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| Pic 1: Drawings on paper/board |
Look at pic 1, what do you see here? A fairly simple drawing - a trapezoid only. However while studying maths, you will have at least the following imaginations in your mind:
1 ) The two diagonals AC and BD and point O - an intersection of them
2 ) The heights AH , BI , CJ and DK
3 ) The midpoints M, N, R and S of AD, BC, AB and CD respectively
4 ) The mid-segment MN
5 ) The intersection point P of the two sides AD and BC
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| Pic 2: The drawing in imagination when looking at the Pic 1 |
If you add a characteristic, such as that trapezoid ABCD is isosceles, then in your visualization there will be the circumcircle (or circumscribed circle) of such trapezoid and its circumcenter! Not to mention the logics & relationship between those factors:
a) The area of a trapezoid = ( AB + CD ) x AH / 2
b ) MN = ( AB + CD ) / 2
c ) AH = BI = CJ = DK
d ) Do you think the points P , R , O , S are on a straight line ?
Pretty impressive isn’t it? This explains why mathematicians need imagination ! Mathematics , problem solving in high school with normal standards (not specialized in mathematics nor with the goal to be a mathematician in the future), if given proper care, can help develop and enrich imaginations naturally!
Khuc Trung Kien
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