![]() In graph-theoretic terms, the theorem states that for loopless planar graph G. In 2005, the theorem was also proved by Georges Gonthier with general-purpose theorem-proving software. To dispel any remaining doubts about the Appel–Haken proof, a simpler proof using the same ideas and still relying on computers was published in 1997 by Robertson, Sanders, Seymour, and Thomas. The four color theorem was proved in 1976 by Kenneth Appel and Wolfgang Haken after many false proofs and counterexamples (unlike the five color theorem, proved in the 1800s, which states that five colors are enough to color a map). The proof has gained wide acceptance since then, although some doubters remain. Initially, this proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand. It was the first major theorem to be proved using a computer. Adjacent means that two regions share a common boundary curve segment, not merely a corner where three or more regions meet. 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. Wi-Fi 802.Statement in mathematics Example of a four-colored map A four-colored map of the states of the United States (ignoring lakes and oceans) LED flash, auto-HDR, HDR10+, stereo sound rec., gyro-EIS & OISġ0 MP, f/2.2, 26mm (wide), 1/3", 1.22µm, Dual Pixel PDAF Octa-core (2x2.73 GHz Mongoose M4 & 2x2.4 GHz Cortex-A75 & 4x1.9 GHz Cortex-A55) - EMEA/LATAM Qualcomm SM8150 Snapdragon 855 (7 nm) - USA/China Stylus, 42ms latency (Bluetooth integration, accelerometer, gyro)Ħ.8 inches, 114.0 cm 2 (~91.0% screen-to-body ratio)ġ440 x 3040 pixels, 19:9 ratio (~498 ppi density)Īndroid 9.0 (Pie), upgradable to Android 12, One UI 4 IP68 dust/water resistant (up to 1.5m for 30 min) ![]() Single SIM (Nano-SIM) or Hybrid Dual SIM (Nano-SIM, dual stand-by) Glass front (Gorilla Glass 6), glass back (Gorilla Glass 6), aluminum frame Versions: SM-N975F (Europe) SM-N975F/DS (Global) SM-N975U (USA) SM-N975U1 (USA unlocked) SM-N975W (Canada) SM-N9750/DS (LATAM, Brazil, China) SM-N975N (South Korea)Īlso known as Samsung Galaxy Note10 Pro Network
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