The Number Devil

The Number Devil: A Mathematical Adventure
– By Hans Magnus Enzensberger

 

 

 

 

 

 

 

 

 

Table of Contents

The First Night: 
1. The importance of 1.
2. Fractions using 1
3. Creating all the whole numbers using only 1 (11×11=1 21)
4. Palindromes and other symmetrical patterns created (111×111=12321, 1111×1111=1234321).
The Second Night:
1. Roman Numerals
2. The importance of zero.
3. Link to negative numbers.
4. Squared numbers & exponents (Hopping)
5. Expanded notation
The Third Night:
1. Division with zero?
2. Prime numbers (Prima donnas).
3. Patterns in primes – any even number larger than 2 is the sum of two prime numbers; any odd number larger than 5 is the sum of 3 prime numbers.
The Fourth Night:
1. Square Roots (Rutabagas)
2. Recurring decimals
The Fifth Night:
1. Triangular Numbers (Coconuts) Any number can be made by adding triangular numbers together.
2. Adding consecutive triangular numbers always results in a squared number.
3. Add consecutive numbers e.g. 1-12 the answer is the 12th triangular number.
The Sixth Night:
1. Fibonacci numbers and sequences (Bonacci). 1,2,3,5,8,13,21…
The Seventh Night:
1. Pascal’s Triangle Relates to triangular numbers
1
1 1
1 2 1
1 3 3 1
The Eighth Night:
1. Permutations and combinations
2. Factorials
3. Circle diagrams.
4. Use of number pyramid for solving problems such as teams of 3, 4, 5 etc
The Ninth Night:
1. Number sequences
• Cardinal
• Odd
• Prime
• Fibonnaci
• Triangular
• Exponents
• Factorial
2. Sum of fractions on a number line ( ½ + ¼ + 1/8 + 1/16 …never equalling 1)
The Tenth Night:
1. Hexagons
2. Fibonacci numbers ÷ them by their neighbours. Recurring decimals
3. 1.618 – the divine proportion
4. Platonic Solids
The Eleventh Night
1. The protagonist wants to do more than play with numbers, he wants to know what’s behind them i.e. the rule of the game. He has become a mathematician.
2. Proof
The Twelfth Night:
1. Famous mathematicians, history of mathematics
2. Pi


Connections
The Joy of Pi