Hobbit Architecture and Pinchbottom's Circumferential Imperative

The astute observer will have noted that, although generally favored throughout most culturally evolved regions of Middle-Earth, there are no straight lines in hobbit architecture. This is principally due to Pinchbottom's Circumferential Imperative, the hobbit-developed algebraic formula (Pi)(rO) (or, colloquially, "Pie-R-Rounded") which holds that the dimensions of any structural feature, when circumferentially biased (or, in layman's terms, "bent") to accommodate the considerable girth of a properly pie-fed-hobbit, must be approximately equal to or greater than (addendum, Bluntskull's Corollary) the cross-sectional sum of the hippopotamus. In practical usage, the principle is applied to entrances, internal doorways and passages, but it is flexible enough to satisfy any project exigency.

Young hobbits learn this geometric fundamental at an early age, since the straight-edge as a learning tool has been largely retired from the elementary classroom in favor of the pin-and-string method of line generation, and is now relegated to the role of disciplinary aid. In fact, logarithmic rather than linear progression lies at the core of hobbit mathematics, although a well-constructed bell curve is held by most non-Cartesian cognoscente in the scientific community to be the quintessential trigonometric plot.

The Pinchbottom principle is grounded in simple expediency, for the hobbit's love of pie is anathema to the pythagorian logic of the acute angle. No square-holes-for-round-pegs in the Shire, although the Sackville-Bagginses are often considered hard-headed enough to have developed a few uncompromising edges. That sentiment aside, Hummel Pinchbottom famously opined at the last Pan-Eriadoran Architects and Tinkers Convention in Bree, after several rather large mugs of rather strong brown ale, "Neither a hippopotamus nor Lobelia Sackville-Baggins should be seriously discomfitted when negotiating a passageway designed in accordance with the Pinchbottom Imperative (hic)!"