Blocks should be composed of straight line segments with preference given to rectangles; a long side to short side ratio of 1.5:1 or greater is also preferred.
In our study, we found the majority of blocks were straight-sided and rectangular. Why? Consider first that rectangles are everywhere. They’re in our buildings, bedrooms, TVs, doorways, drawers, chairs, books, papers, iPhones, parking spaces, shipping boxes, agricultural fields, computers, briefcases, CCDs, and rugs. Rectangles are fairly useful forms for us. The commissioners of Manhattan in 1811 recognized as much saying that "straight-sided and right-angled houses are the most cheap to build and the most convenient to live in."[^Remarks of the Commissioners for Laying out Streets and Roads in the City of New York, Under the Act of April 3, 1807] That statement is as true and relevant today as it was then or as it was 2,000 years ago.
Secondly, we can consider the relative yields of different block geometries (rectangles, irregular angles, triangles, and ovals). We isolated the variable of geometry by holding the area of the blocks constant. We tested the resultant blocks against three different land uses: residential, commercial and parking. We attempted to keep the physical parameters of each land use the same across all he blocks. The results are shown in the table below.
In terms of houses, the rectangular block can accommodate 16 standard house lots, the irregular block can accommodate 15, the triangular can accommodate 14, and the oval can only accommodate 12. The decline in efficiency is easily seen and it continues across all land uses (see the graph below). The further one gets away from the rectangle, the less efficient the block becomes. The reason for this is purely geometrical: there is a "flat packing" efficiency created given all the rectangles we have in our lives. These objects (buildings, beds, books, etc) perfectly pack into corners, leaving no waste of land area. Only few buildings in this world are truly curved: most are actually faceted, meaning they are made up of rectangular building materials (bricks, beams, plywood) that are turned at each juncture along a curve at some desired tolerance.
