Talking about numbers – A mathematical voyage of discovery

What to do without numbers? Communication should be impossible. Numbers play an indispensable role in human communication and economics. Do you want to know something about numbers? In Talking about numbers the author takes you on a mathematical voyage of discovery in number theory.

Title:Talking about numbers, A mathematical voyage of discovery / Over getallen gesproken, Een wiskundige ontdekkingsreis

The Basics:

The motivation to write this book mainly arose from a long mathematical study and interest. The book is split up in four parts. Part I is a personal focus on the author. Because much information is available in both Dutch and English and because this book is a collection of work from a lot of mathematicians, information is provided in both languages. It makes the book accessible for a wide audience.

Summary:

The objective is to open a fascinating and informative world of numbers in number theory. Part II pays attention to early and recent phrases done by wise men, to basic numbers and to numeral systems. An overview of 271 mathematicians from 36 countries and a presentation of mathematical terminology is given, which are part of the descriptions of the number sets in Part III. This part is the lion’s share of the book and includes 465 descriptions of number sets. The description of each number set has been clarified with examples, the name or names of concerned mathematicians together with personal information. To the number sets belong the well-known Natural numbers and Prime numbers. But moreover Achilles numbers, Delannoy numbers, Fibonacci numbers, Lazy caterer numbers, Schizophrenic numbers, Weird numbers and many others are usually unknown. Two number sets:

Delectable numbers

Delectable numbers concern numbers that have 9 digits using them once. The first digit
must be divisible by 1. The first and second digit must be divisible by 2.The first, second and third digit must be divisible by 3, and so on. So far only one Delectable number is known namely 381654729.

3 is divisible by 1
38 is divisible by  2
381 is divisible by  3
3816 is divisible by 4
38165 is divisible by 5
381654 is divisible by 6
3816547 is divisible by 7
38165472 is divisible by 8
381654729 is divisible by 9

Amazing numbers

Discover –1 = +1
-1 = -1
-1/1 = 1/-1
sqrt (-1/1) = sqrt (1/-1)
i/1 = 1/i
i = 1/i
i ∙ i = 1
Ergo: -1 = +1. Fallacy?

Following this, a selection of special numbers with amazing properties is given, followed by a selection of numbers that appear in the Bible and having surprising mathematical relationships. Some examples of special numbers:

Münchhausengetal – Münchhausen number:  3435 = 3³ + 4⁴ + 3³ + 5⁵
Faculteiten – Factorials: 40585 = 4! + 0! + 5! + 8! +5!
Subfaculteiten – Subfactorial:  148349 = !1 + !4 + !8 + !3 + !4 + !9 = 0 + 9 + 14833 + 2 + 9 + 133496

Two examples of Biblical numbers:

17
After the extreme ages named in Genesis 5 the ages dropped considerably. A reference to the patriarchs Abraham, Isaac and Jacob shows the ages and the remarkable prime number 17.

Age
Abraham       : 175 = 7 x 5 x 5 en 7 + 5 + 5 = 17
Izak              : 180 = 5 x 6 x 6 en 5 + 6 + 6 = 17
Jakob            : 147 = 3 x 7 x 7 en 3 + 7 + 7 = 17

 After the extreme ages named in Genesis 5 the ages dropped considerably. A reference to the patriarchs Abraham, Isaac and Jacob shows the ages and the remarkable prime number 17.

22273
The largest Biblical prime number (in Numbers 3).

Finally part III ends with two problems. The first problem (Is P = NP?) is waiting for solution and the second problem (Fermat Point) has already been solved a long time ago.

Part IV includes references to literature and websites. It finishes with two bulky indices of number sets in alphabetical order both in Dutch and English.

Target audience:

Mathematical lecturers, teachers and students and everyone who is interested in or curious about surprising characteristics of numbers. Because the book is written in Dutch and English, besides not a 1:1 translation, the book is not only suitable for the Dutch reader but also for non-Dutch.

Special focus:

The book focuses on 465 number sets part from number theory. The chapters about special numbers and Biblical numbers present an additional view on numbers. Many special numbers are presented like the well-known pi and e, but also numbers in relation to temperature, universe and constants. The chapter about Biblical numbers highlights on numbers that have an explicit mathematical relationship.

Title: Over getallen gesproken, Een wiskundige ontdekkingsreis / Talking about numbers, A mathematical voyage of discovery
ISBN: 9789401800280
Ebook: 9789401806015
Author: Prof. Dr. Ir. Maarten Looijen
Price: € 29,95