Hidden Connections and Double Meanings: A Mathematical Exploration by David Wells

Author:David Wells
Language: eng
Format: epub
Publisher: Dover Publications, Inc.
Published: 2018-07-22T16:00:00+00:00

13

A point of balance

Here is a quadrilateral, a simple geometrical object. If I doodle, as mathematicians sometimes do, and join the mid-points of two opposite sides I can mark X as the 'centre' of the quadrilateral.

It cannot be denied however that this figure does not look very symmetrical. If I continue to doodle by joining the mid-points of the other pair of sides, I shall probably get another, different 'centre'.

Let us do this little experiment. Surprisingly, both points coincide. It seems as if the quadrilateral does have a centre, which I can construct in either of two ways. How can this be? How can I see that this must be so?

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