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4CT Inadequacy Example
In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. ''Adjacent'' means that two regions share a common boundary of non-zero length (i.e., not merely a corner where three or more regions meet). It was the first major theorem to be proved using a computer. Initially, this proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand. The proof has gained wide acceptance since then, although some doubts remain. The theorem is a stronger version of the five color theorem, which can be shown using a significantly simpler argument. Although the weaker five color theorem was proven already in the 1800s, the four color theorem resisted until 1976 when it was proven by Kenneth Appel and Wolfgang Haken in a computer-aided proof. This came after many false proofs and mistaken ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Four Colour Map Example
4 (four) is a number, numeral (linguistics), numeral and numerical digit, digit. It is the natural number following 3 and preceding 5. It is a square number, the smallest semiprime and composite number, and is tetraphobia, considered unlucky in many East Asian cultures. Evolution of the Hindu-Arabic digit Brahmic numerals represented 1, 2, and 3 with as many lines. 4 was simplified by joining its four lines into a cross that looks like the modern plus sign. The Shunga Empire, Shunga would add a horizontal line on top of the digit, and the Northern Satraps, Kshatrapa and Pallava dynasty, Pallava evolved the digit to a point where the speed of writing was a secondary concern. The Arabs' 4 still had the early concept of the cross, but for the sake of efficiency, was made in one stroke by connecting the "western" end to the "northern" end; the "eastern" end was finished off with a curve. The Europeans dropped the finishing curve and gradually made the digit less cursive, endi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
