A Mathematical Drama in Three Acts (pp.xvi + 383)

2. e, i & pi:  A MATHEMATICAL DRAMA IN THREE ACTS (pp.xvi + 383)

This  book  presents  a  new  concept  in  teaching  mathematics,  focussing  on  the  key  numbers  e,  i  and  pi,  and showing  how  the  central  concepts  develop  one  from  the  other  and  interweave,  as  described  in  BW/003. It  is  intended  for  a  wide  readership,  including  particularly  people  of  normal  intelligence  who  because badly taught at school decided prematurely that maths was ‘not for them.’ As it says in the Introduction: This  book  is  intended  for  anyone  who  wants  to  learn,  or  refresh  their  understanding  of,  some  of  the basic  elements  of  mathematics  and  how  they  relate  to  each  other. It  differs  from  conventional  texts primarily  in  terms  of  the  sequence  in  which  its  material  is  presented,  and  in  the  connecting  threads between  topics. Where  possible,  it  seeks  to  present  mathematics  in  the  order  in  which  mankind discovered  it,  giving  passing  references  to  the  discoverers  of  particular  branches  as  it  does  so,  and showing how one discovery led to the next.As  a  result,  at  whatever  point  a  student  leaves  the  course,  he  or  she  ought  to  have  acquired  a  body  of knowledge which has a definite beginning and progresses intelligibly towards a definite end.In  particular,  we  celebrate  in  this  book  the  Swiss  mathematician  Leonhard  Euler  (pronounced  “oiler”) (1707-1783),  surely  the  greatest  mathematician  of  the  eighteenth  century  and  unquestionably  one  of the  greatest  of  all  time. As  Laplace  said  of  him,  ‘He  is  the  master  of  us  all.’  Euler’s  celebrated  unification of  trigonometry,  complex  numbers,  and  exponentials,  described  in  his  Introductio  in Analysin  Infinitorum (1744,  published  1748),  takes  us  to  the  climax  of  this  book.  In  it  he  brings  together  the  three  most fundamental constants around which this book is based:e : central to logarithms, exponentials and the calculus,i : central to complex numbers, andpi : central to trigonometry (and much else). 

From this follows what is probably the most beautiful and astonishing equation in all mathematics:ei.pi + 1 = 0 or, re-expressed, ei.pi = -1This book attempts to chart the path which leads to that climax.In  addition  it  touches  on  the  philosophy  of  mathematics,  commenting  from  time  to  time  on  the  famous  debate as to maths is discovered or invented.The book can be downloaded in its entirety as a PDF free of charge by clicking here.

The    Microsoft    QuickBASIC    utilities    RECIP.EXE,    POLYDIV.EXE,    POLYDIV2.EXE,    CONFRA.EXE    and CONRAD.EXE,  together  with  the  Microsoft  Excel  spreadsheet  BINOM.XLS,  which  accompany  the  book  and are described in it, can be downloaded as a .zip file by clicking here.