When Texas sought to enter the Union in 1845 as a slave state, federal law in the United States, based on the Missouri Compromise, prohibited slavery north of 36°30' parallel north. Under the Compromise of 1850, Texas surrendered its lands north of 36°30' latitude. The 170-mile strip of land, a "neutral strip", was left with no state or territorial ownership from 1850 until 1890. It was officially called the "Public Land Strip" and was commonly referred to as "No Man's Land."
Also explained in that show. The borders are rough on the East because they were based on rivers and geographic features. As we moved West we invented and introduced railroads and those became our new borders hence the squareness.