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In Thomas Jefferson’s imperial imagination, the trans-Appalachian West would be made American by geometry. The West’s conquest (and conversion into real estate) was begun when Congress adopted Jefferson’s scheme to lay over the disorderly wilderness his rigidly orthogonal grid of township and range. The Land Ordinance of 1785 called for subdividing federal land into square townships consisting of thirty-six one-square-mile sections, later defined by Congress as 640 acres each. The Homestead Act of 1862 extended the logic of this system to thousands of immigrant farmers west of the Mississippi by granting each head of household a quarter section (one-quarter of 640 acres, or 160 acres). A “forty” is forty acres, or one-sixteenth of a section. Sections in a township are numbered from east to west and then from west to east, turning back at the end of each row of six sections. This pattern is called boustrophedonic, meaning “turning like oxen in plowing.” Roads, city and county limits, and private property lines in the West often follow the Jeffersonian grid. These section and township lines cross mountain ranges and deserts, blind to history and natural features. A geometric mindset on the part of eastern lawmakers is why so many western states have sharp corners.

D. J. Waldie