Quadripoint
The Four Corners Monument is the only point in the United States where four states meet: Colorado, Utah, New Mexico, and Arizona meet at right angles. The United States first acquired the area now called Four Corners from Mexico after the Mexican–American War in 1848. In 1863 Congress created Arizona Territory from the western part of New Mexico Territory. The boundary was defined as a line running due south from the southwest corner of Colorado Territory, which had been created in 1861. By defining one boundary as starting at the corner of another Congress ensured the eventual creation of four states meeting at a point, regardless of the inevitable errors of boundary surveying. The monument is centered at .
Conjecture
In mathematics, the four color theorem, or the four color map theorem, states that, given any separation of a plane into contiguous regions, producing a figure called a "map", no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color. Two regions are called "adjacent" if they share a common boundary that is not a corner, where corners are the points shared by three or more regions. For example, in the map of the United States of America, Utah and Arizona are adjacent, but Utah and New Mexico, which only share a point that also belongs to Arizona and Colorado, are not.