The match between Portugal and Brazil yesterday night inspired me something.
I see the “Four Colors Problem” there!
And, YES. I heard Cristiano Ronaldo asked the people there why at most 4 colors are needed to color the subsurfaces of football such that any two neighboring subsurfaces are colored differently.
“Why not more than 4 colors? What is the proof?”, Ronaldo asked the FIFA officer.
A little history – Augustus De Morgan, a professor in University College, London first discussed (gossip?) the four colors problem with his friend Sir William Rowan Hamilton in 1852. Since then many proofs have been proposed but there isn’t any proof that explains the theorem beautifully (my believe).
My salutation to Edward Lorenz, the founder of Chaos Theory. These graphs are generated through Python and SciPy. Try dumping the following codes into the IPython and have fun changing the view of the Lorenz attactor.
There are two famous IEEE standards for mesh technology – IEEE 802.15.3x for high-rate WPAN and IEEE 802.15.4x for low-rate WPAN. Question is always arisen on the interoperability between these two standards. To answer that question, IEEE has introduced a new standard, IEEE 802.15.5 that is built on the mesh sublayer on top of both IEEE 802.15.3x and IEEE 802.15.4x (refer to the figure).
More discussion on such standard can be found in IEEE Communication magazine in .
 M. Lee, R. Zhang, C. Zhu, T. R. Park, C. S. Shin, Y.A. Jeon, S. H. Lee, S. S. Choi, Y. Liu, S. W. Park, “Meshing Wireless Personal Area Networks: Introducing IEEE 802.15.5”, IEEE Communication Magazine, January 2010, page 54 – 61.