Science and Education Publishing American Journal of Mathematical Analysis 2333-8431 3 3 2015 09 15 On Geometrical Methods that Provide a Short Proof of Four Color Theorem 65 71 EN BAHMAN MASHOOD La Playa Street. 304. San Francisco.CA 94109, US AJMA2015332 10.12691/ajma-3-3-2 2015 06 17 2015 07 04 2015 09 15 In this article we introduce a short and comprehensive proof of four color theorem based on geometrical methods. At the end of the article we will provide a short proof of the De Bruijn Erdos theorem for locally finite infinite graphs.