By Committee on the Mathematical Sciences in 2025; Board on Mathematical Sciences and Their Applications; Division on Engineering and Physical Sciences; National Research Council 191 pages, Published 2013, National Academies Press, Washington, USA. ISBN: 0309268796   The Mathematical Sciences in 2025, a new report from the National Research Council, finds that the mathematical...

The Best Writing on Mathematics 2011 Paperback, 383 pages, Published November 7, 2011 Princeton University Press, ISBN: 0691153159.   The Best Writing on Mathematics 2012 Paperback, 288 pages, Published October 22, 2012 Princeton University Press, ISBN: 0691156557.   These two volumes of anthology bring together from around the world the finest mathematics writing in the years 2011...

Burkard Polster and Marty Ross Johns Hopkins University Press, 2012, ISBN: 978-1-4214-0483-7 (hardback) Also available in paperback (ISBN: 978-1-4214-0484-4) and for Kindle   This is an entertaining grab bag of mathematical and movie titbits that will delight mathematically minded movie buffs. The authors also have a website that includes links to...

IT IS VERY INTERESTING TAKE ANY NUMBER OF DIGITS. HERE I AM TAKING 25 AND 32
  • YOU CAN WRITE THEM IN FOUR WAYS LIKE THAT(25*32/25*23/52*23/52*32)

25*32=800

25*23=575

52*23=1196

52*32=1664

  • SUBTRACT BIGGER ONE TO ANY LOWER, ONE BY ONE

1664-1196=468=4+6+8=­18=1+8=9

1664-575=1089=1+0+8+­9=18=1+8=9

1164-800=864=8+6+4=1­8=1+8=9

1196-575=621=6+2+1=9

1196-800=396=3+6+9=1­8=1+8=9

800-575=225=2+2+5=9

Always THE SUM IS 9. IT IS TRUE FOR ANY DIGITS..

1. Introduction Fixed point theory is very simple, but is based on fundamentals in Mathematics. For any continuous function $$f:Xrightarrow X$$ a fixed point of $$f$$ is a point $$xin X$$ satisfying the identity $$f(x)=x.$$ Two fundamental theorems concerning fixed points are Banach Theorem and Brouwer Theorem. Banach theorem states that if $$X$$ is a complete metric space and $$f$$ is a contraction then $$f$$ has a unique fixed point. In Brouwer theorem, $$X$$ must be the closed unit ball in a Euclidean space. Then any $$f$$ has a fixed point. But in this case, the set of fixed points is not necessarily a one-point set. In Banach theorem, a metric on $$X$$ is used in the crucial assumption that $$f$$ is a contraction. The unit ball in a Euclidean space is also a metric space and the metric topology determines the continuity of continuous functions, however the essence of Brouwer theorem is a topological property of the unit ball, namely the unit ball is compact and contractible. Banach theorem and Brouwer theorem tell us a difference between two major branches of fixed point theory, metric space fixed point theory and topological fixed point theory. It is impossible to distinguish two fixed point theories in an exact way, and it is not easy to determine a certain topics belong to which branch. In general, the fixed point theory is regarded as a branch of topology. But due to deep influence on topics related to nonlinear analysis or dynamic systems, many parts of the fixed point theory can be considered as a branch of analysis.