Figurate NumbersElena Deza and Michel Marie Deza World Scientific, 2011, xviii+456 pp.   This book is about special types of numbers (integers) that have geometric associations and that have intriguing spatial properties. The ancient Greeks were perhaps the first to study what are called “figurate numbers” — numbers that can be represented by regular geometric patterns of points in the plane or in space, such as triangular, polygonal and polyhedral numbers. The first two chapters contain a lot of formulae for all kinds of figurate numbers that arise from geometric patterns in 2 and 3 dimensions. Properties and relations between such figurate numbers and their connections with Diophantine equations have been studied by classical mathematicians like Euler, Fermat, Lagrange, Legendre, Cauchy, Gauss and Dirichlet. Chapter 3 extends the construction of figurate numbers to dimension 4 and beyond. Examples of such numbers are the pentatope numbers which are 4-dimensional analogues of triangular and tetrahedral numbers, and the biquadratic numbers which are the 4-dimensional analogues of square and cubic numbers. Despite the lack of visual pictures and physical intuition, multitudes of formulae are presented and proved.

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..