I heard on several earlier episodes of the RRS that a circle is not a square.  I wanted to say that if you speak of a circle in Euclidean geometry, then a circle is not a square, but if you move outside of geometry a circle can be square.  If you have a globe, you can draw a triangle on it with three 90 degree corners, two corners on the equator and one on a pole, but this is a Reimannian geometry.  Algebraically a circle is defined as the collection of points (locus) whic are equidistant from a single point.  The concept of distance in mathematics is formalized with something called a metric, a metric is a unique value describing how far two points are from one another; the distance is always positive or zero, the distance of a point to itself is zero, and the distance from point A to C is less than or equal to the distance from A to B plus B to C.

Now, to imagine a legitimate (mathematical) square circle, imagine a grid block system aligned with the cardinal compass directions.  Each block is of equal width in the north-south and east-west directions, all streets intersect at 90 degree angles.  Suppose you only measure distance by the largest number of blocks you travel in one of the cardinal directions, so if you travel east 5 blocks and north 6 blocks, then you would have traveled 6 blocks in this way of measuring.   If you pick a number of blocks, say 6 blocks and draw a line connecting all points that are 6 blocks away, you have a square circle.

 I think my point is that we should be very careful to avoid using the trite quips that appeal to our innate sense of what is correct because it often hinges on definitions.