Mathematical adventures sometimes lurk where we least expect them—even in a spider's web. It all begins with a square forming the web's frame. The arachnid starts on the left side at A0, then moves clockwise to the midpoints of the adjacent sides. Admittedly, a real spider would not go about it this way (see Mathématiques et Biologie, Bibliothèque Tangente 42), but ours is a mathematical spider! After all, this construction is as good as any other, and its simple geometric rule offers a pleasant diversion.
As the drawing progresses, it becomes clear that the spider is heading towards a very specific point on its web. In other words, it seems to converge! This opens the door to an investigation that will take us on a pleasant tour through the landscape... of linear algebra.
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The vector space of webs
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