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Generalizations of the geometric construction that repeatedly
attaches rectangles to a square, originally given by Myerson, are presented.
The initial square is replaced with a rectangle, and also the dimensionality of
the construction is increased. By selecting values for the various parameters,
such as the lengths of the sides of the original rectangle or rectangular box
in dimensions more than two and their relationships to the size of the attached
rectangles or rectangular boxes, some interesting formulas are found. Examples
are Wallis-type infinite-product formulas for the areas of p-circles with p > 1.
The normal direction to the normal direction to a line in Minkowski
geometries generally does not give the original line. We show that in lp geometries with p>1 repeatedly
finding the normal line through the origin gives sequences of lines that
monotonically approach specific lines of symmetry of the unit circle. Which
lines of symmetry that are approached depends upon the value of p and the slope of the initial line.