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.
Despite the motivation from coloring political maps of countries, the theorem is not of particular interest to mapmakers. According to an article by the math historian Kenneth May (Wilson 2014, 2), “Maps utilizing only four colors are rare, and those that do usually require only three. Books on cartography and the history of mapmaking do not mention the four-color property.”
Three colors are adequate for simpler maps, but an additional fourth color is required for some maps, such as a map in which one region is surrounded by an odd number of other regions that touch each other in a cycle. The five color theorem, which has a short elementary proof, states that five colors suffice to color a map and was proven in the late 19th century (Heawood 1890); however, proving that four colors suffice turned out to be significantly harder. A number of false proofs and false counterexamples have appeared since the first statement of the four color theorem in 1852.
Actors: Elijah Wood (actor), Burnie Burns (actor), Burnie Burns (director), Burnie Burns (writer), Burnie Burns (actor), Burnie Burns (actor), Burnie Burns (actor), Nathan Zellner (actor), Matt Hullum (actor), Matt Hullum (actor), Matt Hullum (actor), Matt Hullum (actor), Matt Hullum (writer), Matt Hullum (director), Chris Demarais (actor),
Plot: Witness the gripping and hilarious finale to the Project Freelancer saga, complete with newly animated battle sequences. The world's longest-running web series ever of all time, set in the universe of the enormously popular video game franchise Halo.
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Plot: The classic Twain story "The Prince and the Pauper" gets a modern slant when Prince Edward of Gelfland switches places with Southern California surfer Cash Canty. Both discover a new world of romance, danger, and adventure beyond their wildest dreams.
Keywords: family-relationships, identity-swap, prince, surfer, teen-angstWatching me fall
Into the flames
Of a broken soul tonight
No stone overturned
This graveyard of mine
Allows me no peace
[Chorus]
Sleep as day dies
Sleepwalk with the dead
Wander aimlessly through the night
Love and regret
Course through my veins
As I slowly fade away
Please let me sleep
Just one last night
Before I must wake
[Chorus]
And I walk with these ghosts
And I walk with these ghosts
And I walk with these ghosts...
[Chorus]
Sleep as night falls
Sleepwalk with the dead
Hope keeps me alive
Radio Free Europe | 17 Sep 2018
The Independent | 17 Sep 2018
WorldNews.com | 17 Sep 2018
WorldNews.com | 17 Sep 2018
WorldNews.com | 17 Sep 2018
WorldNews.com | 17 Sep 2018