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.