The Geometry of K'Nex

The K'Nex building system is composed of a fixed set of pieces that might appear to have mysterious size relationships. The goal of this page is to identify the geometric relations among the pieces that contribute the the way the pieces can be combined to produce structures.

An important aspect of the pieces is the use of 45, 90, and 180 degree angles. All joints and connections use these angles to form triangles, rectangles, and squares. In addition, since the triangles are right isoceles only (angles of 45-45-90), the length relation between two colors of pieces is required to be related by a factor of the square root of 2 (approximately 1.414). I'll here after refer to the square root of 2 as "sqrt(2)"

So, for example, the blue sticks implement the hypotenuse, which two white sticks implement the legs. Thus the blue stick is sqrt(2) times the white stick in length. The same relation applies to these pairs:

This tidy radial pattern nicely illustrates the relations in a single structure.

A complexity is that the stick lengths are added to a small bias that is part of the joints, so some kinds of connections cannot be made to fit by adding different sticks end to end with a coupler. More to come on this issue....

Meanwhile, enjoy a few images that illustrate the relations mentioned above:
white-green,blue-white,yellow-blue
red-yellow
gray-red


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Ralph L. Vinciguerra - 2002-01-15