## 09 SepFigurate Numbers

Elena 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.

## 09 SepUnderstanding Probability (3rd Edition)

Henk Tijms Cambridge University Press, 2012, 572 pp.   The third edition of “Understanding Probability” by Henk Tijms is an introductory book on probability theory. It is written at the level at which one requires, at most, a first course in calculus to read it. The book is...

## 09 SepThe Mathematical Sciences in 2025

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...

## 09 SepCounting (2nd Edition)

Koh Khee Meng and Tay Eng Guan. World Scientific, 2013, xii+209 pp   This book is about the art of counting using some basic principles of combinatorial mathematics. It starts from scratch and is meant for students and teachers at the upper secondary and undergraduate level. This second...

## 09 SepThe Best Writing on Mathematics 2011 and 2012

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...

## 09 SepHandbook of Cubik Math

Alexander H. Frey, Jr and David Singmaster. Lutterworth Press (an imprint of James Clarke & Co Ltd), 2010, ISBN: 978-0-71-889209-8   The Rubik’s Cube arrived in Australia in about 1980 and started a craze remembered by many. Books presenting easy-to-follow algorithms for solving the cube (for example, Taylor [4])...

## 09 SepMath Goes to the Movies

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...

## 07 SepMathematical Quest 4: More about Primes

The following was published in Young NE, Vol. 1, Issue 5 (September 2013). We thank the editor of Young NE for permission to post this here.

## 05 SepAmazing Number Nine

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..

## 05 SepVideo Lecture on Numbers

The editor of the English section of this website gave a video lecture for school students of Podar International School in Mumbai. The video can be seen below. [ad#ad-2]...