I don't know what to tell her about the body... JK I don't have anything in my copy and paste... Sent from my iPhone using Tapatalk
Almost your birthday get ready for ur birthday wishes lid Lols Go outside your house wtf noty now turn around clap That's Sarah talking clap no its not spellcheck meant to say my sis How lol zxdfvghjkl; dxfguhik dfgyuhikl dfxghjkl; fcghjkl fcghjkl drtuyio; soz that was my sis fghjkl]\ ] ewfgbxiope tgmjnry \342r by e uj5 dfgi Stop it 0:08 um ok Yeaokay Yea Sarah weirdo whoops meant to sya im weirdo Looking forward to not being a twelve vie anymore in like 2 hours yeah Yea What for ur post at 12:am what lol Your birthday wishes at 12 nO Well u should be whoops wrong person Sarah stop typing!!!! w h s a t a b c d e f g h i j k l m n o p q Let's send letters off the alphabet r s t u v w x y z NO GO AWYAYYY DONE Chat Conversation End a one way conversation i got spammed with
The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not share the same color. This problem is sometimes also called Guthrie's problem after F. Guthrie, who first conjectured the theorem in 1852. The conjecture was then communicated to de Morgan and thence into the general community. In 1878, Cayley wrote the first paper on the conjecture. Fallacious proofs were given independently by Kempe (1879) and Tait (1880). Kempe's proof was accepted for a decade until Heawood showed an error using a map with 18 faces (although a map with nine faces suffices to show the fallacy). The Heawood conjecture provided a very general assertion for map coloring, showing that in a genus 0 space (including the sphere or plane), four colors suffice. Ringel and Youngs (1968) proved that for genus , the upper bound provided by the Heawood conjecture also give the necessary number of colors, with the exception of the Klein bottle(for which the Heawood formula gives seven, but the correct bound is six). Six colors can be proven to suffice for the case, and this number can easily be reduced to five, but reducing the number of colors all the way to four proved very difficult. This result was finally obtained by Appel and Haken (1977), who constructed a computer-assisted proof that four colors weresufficient. However, because part of the proof consisted of an exhaustive analysis of many discrete cases by a computer, some mathematicians do not accept it. However, no flaws have yet been found, so the proof appears valid. A shorter, independent proof was constructed by Robertson et al. (1996; Thomas 1998). In December 2004, G. Gonthier of Microsoft Research in Cambridge, England (working with B. Werner of INRIA in France) announced that they had verified the Robertson et al. proof by formulating the problem in the equational logic program Coq and confirming the validity of each of its steps (Devlin 2005, Knight 2005). J. Ferro (pers. comm., Nov. 8, 2005) has debunked a number of purported "short" proofs of the four-color theorem. Was doing a math assignment...
When the hell did exponents get so detailed as to require an essay to solve for X? Damn common core math! D:<
