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6. Geometry

6. Geometry  

Timothy Gowers

in Mathematics: A Very Short Introduction

Print Publication Year: 
Aug 2002
Published Online: 
Sep 2013
eISBN: 
9780191776397
DOI: 
10.1093/actrade/9780192853615.003.0006
Item type: 
chapter
ISBN: 
9780192853615
‘Geometry’ begins with the Euclidean geometry, the geometry with which most people are familiar. Euclid's Elements, written in around 300bc, started with five axioms from which Euclid ... More
3. Perfect and not so perfect numbers

3. Perfect and not so perfect numbers  

Peter M. Higgins

in Numbers: A Very Short Introduction

Print Publication Year: 
Feb 2011
Published Online: 
Sep 2013
eISBN: 
9780191777820
DOI: 
10.1093/actrade/9780199584055.003.0003
Item type: 
chapter
ISBN: 
9780199584055
‘Perfect and not so perfect numbers’ examines the concept of perfect numbers. Perfect numbers are numbers which are the sum of their proper factors. Euclid showed that perfect numbers had a ... More
Applied Mathematics: A Very Short Introduction

Applied Mathematics: A Very Short Introduction  

Alain Goriely

Print Publication Year: 
Feb 2018
Published Online: 
Feb 2018
eISBN: 
9780191815805
DOI: 
10.1093/actrade/9780198754046.001.0001
Item type: 
book
ISBN: 
9780198754046
Mathematics is playing an increasingly important role in society and the sciences, enhancing our ability to use models and handle data. Applied Mathematics: A Very Short Introduction ... More
6. The Structure of the Sciences

6. The Structure of the Sciences  

Jonathan Barnes

in Aristotle: A Very Short Introduction

Print Publication Year: 
Oct 2000
Published Online: 
Nov 2015
eISBN: 
9780191822322
DOI: 
10.1093/actrade/9780192854087.003.0006
Item type: 
chapter
ISBN: 
9780192854087
Aristotle did not share Plato’s belief that all knowledge could be founded upon a single set of axioms. ‘The Structure of the Sciences’ shows that Aristotle divided knowledge into three ... More
4. Identities, and more identities

4. Identities, and more identities  

Glen Van Brummelen

in Trigonometry: A Very Short Introduction

Print Publication Year: 
Jan 2020
Published Online: 
Jan 2020
eISBN: 
9780191851896
DOI: 
10.1093/actrade/9780198814313.003.0004
Item type: 
chapter
ISBN: 
9780198814313
The world of trigonometry is full of identities: some of them extremely useful, others beautiful, and a few that are simply bizarre. ‘Identities, and more identities’ takes a tour of the ... More
4. Limits and infinity

4. Limits and infinity  

Timothy Gowers

in Mathematics: A Very Short Introduction

Print Publication Year: 
Aug 2002
Published Online: 
Sep 2013
eISBN: 
9780191776397
DOI: 
10.1093/actrade/9780192853615.003.0004
Item type: 
chapter
ISBN: 
9780192853615
In one way or another, the concept of infinity is indispensable to mathematics, and yet it is a very hard idea to make rigorous. ‘Limits and infinity’ discusses three statements that each ... More
Mathematics: A Very Short Introduction

Mathematics: A Very Short Introduction  

Timothy Gowers

Print Publication Year: 
Aug 2002
Published Online: 
Sep 2013
eISBN: 
9780191776397
DOI: 
10.1093/actrade/9780192853615.001.0001
Item type: 
book
ISBN: 
9780192853615
The aim of Mathematics: A Very Short Introduction is to explain, carefully but not technically, the differences between advanced, research-level mathematics, and the sort of mathematics we ... More
2. The unending sequence of primes

2. The unending sequence of primes  

Peter M. Higgins

in Numbers: A Very Short Introduction

Print Publication Year: 
Feb 2011
Published Online: 
Sep 2013
eISBN: 
9780191777820
DOI: 
10.1093/actrade/9780199584055.003.0002
Item type: 
chapter
ISBN: 
9780199584055
‘The unending sequence of primes’ asks: How can we be sure that primes do not become extinct? A number of mathematical proofs have shown this. It can easily be shown that all primes are ... More
1. What is symmetry?

1. What is symmetry?  

Ian Stewart

in Symmetry: A Very Short Introduction

Print Publication Year: 
May 2013
Published Online: 
Sep 2013
eISBN: 
9780191778292
DOI: 
10.1093/actrade/9780199651986.003.0002
Item type: 
chapter
ISBN: 
9780199651986
The concept of symmetry can be defined as a transformation of a mathematical structure, of a specified kind, that leaves specified properties of the structure unchanged. However, because a ... More
5. Geometric infinity

5. Geometric infinity  

Ian Stewart

in Infinity: A Very Short Introduction

Print Publication Year: 
Mar 2017
Published Online: 
Mar 2017
eISBN: 
9780191816574
DOI: 
10.1093/actrade/9780198755234.003.0006
Item type: 
chapter
ISBN: 
9780198755234
Much of the philosophical and mathematical fun comes from trying to tease the different meanings apart, and deciding which make sense, and why. A clear example occurs in ‘Geometric ... More
1. What’s so funny ‘bout applied mathematics? Modelling, theory, and methods

1. What’s so funny ‘bout applied mathematics? Modelling, theory, and methods  

Alain Goriely

in Applied Mathematics: A Very Short Introduction

Print Publication Year: 
Feb 2018
Published Online: 
Feb 2018
eISBN: 
9780191815805
DOI: 
10.1093/actrade/9780198754046.003.0001
Item type: 
chapter
ISBN: 
9780198754046
What is applied mathematics and how is it different from mathematics or any other scientific discipline? ‘What’s so funny ‘bout applied mathematics? Modelling, theory, and methods’ argues ... More
1. Copernicus, the young scholar

1. Copernicus, the young scholar  

Owen Gingerich

in Copernicus: A Very Short Introduction

Print Publication Year: 
Aug 2016
Published Online: 
Aug 2016
eISBN: 
9780190605520
DOI: 
10.1093/actrade/9780199330966.003.0002
Item type: 
chapter
ISBN: 
9780199330966
Nicolaus Copernicus was born in Torun, Poland, on February 19, 1473. When his father died in 1483, his maternal uncle, Lucas Watzenrode (who became bishop of Varmia in 1489), took over ... More
3. Algorithmic thinking

3. Algorithmic thinking  

Subrata Dasgupta

in Computer Science: A Very Short Introduction

Print Publication Year: 
Mar 2016
Published Online: 
Mar 2016
eISBN: 
9780191798146
DOI: 
10.1093/actrade/9780198733461.003.0003
Item type: 
chapter
ISBN: 
9780198733461
Algorithms are at the epicentre of computer science—thinking computationally is forming the habit of algorithmic thinking. In order for a procedure to qualify as an algorithm, it must ... More
2. Multiplying and dividing

2. Multiplying and dividing  

Robin Wilson

in Number Theory: A Very Short Introduction

Print Publication Year: 
May 2020
Published Online: 
May 2020
eISBN: 
9780191839351
DOI: 
10.1093/actrade/9780198798095.003.0002
Item type: 
chapter
ISBN: 
9780198798095
‘Multiplying and dividing’ looks at multiples and divisors, focusing on the least common multiple and greatest common divisor of two numbers. We use Euclid’s algorithm as a method for ... More
Numbers: A Very Short Introduction

Numbers: A Very Short Introduction  

Peter M. Higgins

Print Publication Year: 
Feb 2011
Published Online: 
Sep 2013
eISBN: 
9780191777820
DOI: 
10.1093/actrade/9780199584055.001.0001
Item type: 
book
ISBN: 
9780199584055
Numbers: A very Short Introduction unravels the world of numbers; demonstrating its richness, and providing a comprehensive view of the idea of the number. This VSI paints a picture of the ... More
Number Theory: A Very Short Introduction

Number Theory: A Very Short Introduction  

Robin Wilson

Print Publication Year: 
May 2020
Published Online: 
May 2020
eISBN: 
9780191839351
DOI: 
10.1093/actrade/9780198798095.001.0001
Item type: 
book
ISBN: 
9780198798095
Number Theory: A Very Short Introduction explains the branch of mathematics primarily concerned with the counting numbers, 1, 2, 3, …. Long considered one of the most ... More

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