history of mathematics - National STEM Centre

10.1
Visualising
negative numbers
10.2
Subtracted numbers
are more acceptable
10.5
A geometrical
argument
10.7
The equivalence of
the different cases
10.9
Negative numbers I
and the number line
10.10
Objections to
negative numbers'':
10.11 n
A debate about ;
negative numbers;*
124
'Two minuses make a plus'
10.3
A Chinese
livestock problem
10.6
The Greek
version
10.8
Why a lapse
in developnea.fl.
In this chapter, you will learn about the struggle that mathematicians had, first, with
accepting negative numbers and, secondly, with the idea that 'minus x minus makes
a plus'.
10.4
The Chinese rules
Even though you may yourself be quite at ease
using negative numbers, you will see in this chapter
that the concept created controversy and objections
from the very earliest times. It is only
comparatively recently, in the last century or so,
that mathematicians have accepted negative numbers as a proper part of
mathematics. Even now, many people struggle to make sense of them.
As you read about the objections to negative numbers, you may find
yourself sympathising with those who raised the objections in the first
place. You may also see that there is more to negative numbers than you
might previously have realised.
Activities 10.1 and 10.2, together with the optional activities 10.3 and 10.4, are
about negative numbers and the ways that people thought about them.
The remaining activities, including the optional activities, 10.6 and 10.8, show the
way that people thought about carrying out arithmetic operations with negative
numbers, and how they 'explained' their ideas.
In Activity 10.11, you will be asked to take part in a debate about 'two minuses
make a plus', so you should, if you can, work on it in a small group.
All the activities are suitable for working in a small group.
Activities 10.3,10.4,10.6 and 10.8 are optional.
Work on Activity 10.11 in a small group if you can.
Work through the activities in sequence.
Negative numbers
Activity 10.1 Visualising negative numbers
1 You already have different ways of thinking about and visualising negative