The Semi-Perimeter of a rectangle is equal to half the perimeter, that is width plus height
In squared rectangle theory the semi-perimeter of a squared rectangle is related to the number of spanning trees in the rectangles 'Smith Diagram' (a planar graph where edges represent squares). Certain numbers appear as the semi-perimeter in a given order and then reappear in the next highest order as square sizes. For example, one finds that four of the six simple perfect rectangles of order 10 have semi-perimeter 209, and that five of the 22 simple perfect rectangles of order 11 have 209 as a side. When Brooks, Smith, Stone and Tutte researched squared rectangles they called this 'the law of unaccountable recurrence'. After they made the connection between square tiling and planar electrical networks they were able to explain this phenomenon. As Tutte wrote, "if two squared rectangles correspond to networks of the same structure, differing only in the choice of poles, then the full horizontal sides are equal. Further if two rectangles have networks which acquire the same structure when the two poles of each are identified, then the full horizontal sides are equal. Further, if two rectangles have networks which acquire the same structure when the poles of each are identified, then the two vertical sides are equal. These two facts explained all the cases of 'unaccountable recurrence' which we had encountered."
SPSRs from orders 9 to 17 are sorted by Semi-Perimeter. o9-17spsr-w+h.csv
format; (width+height) (width-height) (widthxheight) (width/height) order width height e1 e2 e3 ... en (elements in bouwkamp code order);
for example 65 1 1056 1.03 9 33 32 9 10 14 8 1 7 4 18 15