Horseman, 1946 Maths is Everywhere

Art Tessellation is the process of
tiling a space with congruent
M. C. Escher, Horseman, 1946 (identical) shapes.

Maths is Everywhere

Art

Patrick Seymour, Faces Reflection and
rotation
symmetry can
be found in
art and
nature.

Maths is Everywhere

Art

Drawing with a
vanishing point to
create perspective
was first explained
by mathematicians
and geometers in
the 15th century.

Maths is Everywhere

Business

Calculating profit
and loss, projecting
sales, setting
targets, interpreting
figures: these are
all essential parts
of any business.

Maths is Everywhere

Computing

Computers run on tiny
circuits that have two
states: on or off. Each
state is represented by
either 1 (on) or 0 (off).
This means any calculations
are done with these binary
numbers and the entire
system is built upon
calculations in binary.

Maths is Everywhere

Computing

Disk space is calculated as powers
of 2:

1 bit = 1 or 0 (on or off)
1 nibble = 4 (22) bits
1 byte = 8 (23) bits
1 kilobyte = 1024 (210) bytes
1 megabyte = 1024 (210)
kilobytes or 220 bytes
1 gigabyte = 1024 megabytes, or
230 bytes
1 terabyte = 1024 gigabytes, or
240 bytes

Maths is Everywhere

Computing

Computer programming
is written with
algorithms, which follow
the rules of
mathematical logic.

Maths is Everywhere

Computing

All motion of objects in
computer games is
calculated using
mathematical
equations, which are
most often quadratic.

Maths is Everywhere

Computing

So much animation
uses mathematics, from
Bézier curves to draw
moving grass, to
combinatorics to
design hundreds of
robots from just a few
component parts.

Maths is Everywhere

Economics

The worldwide
monetary system
relies on complex
calculations and
statistics.

Maths is Everywhere

English

These literary works all contain elements of
mathematics, and are all notable in their genres.

Maths is Everywhere

English In any book or collection of written works

the most common word will probably be

the. The second most common word would
ଵ
be of and this is used ଶ as often as the, the

third most common would be to and this is
ଵ
used ଷ as much as the, the fourth most

common would be and and this is used ଵ as
ସ
much as the. This pattern continues

indefinitely and, remarkably, is true for

both written and spoken language!

This amazing rule is called Zipf’s Law and
actually holds for all languages!

Maths is Everywhere

Food

Understanding of ratio
and proportion, and
good mental arithmetic,
are essential when
making changes to
recipes to cater for
larger or smaller groups
of people.

Maths is Everywhere

Food Quality control in food
technology is often conducted
using statistics and the normal
distribution. For instance, if a
jar claims to contain 300g of
sauce, the machine may be set
so that 90% of jars contain
between 290g and 310g.

Maths is Everywhere

Geography

Surveying equipment,
used to determine
features of the landscape,
such as heights of
mountains, is created
using mathematics,
especially trigonometry.

Maths is Everywhere

Geography

Human geography
involves studying patterns
in populations and
settlements, and requires
use of lots of statistics to
analyse what is observed.

Maths is Everywhere

Geography

Map reading involves the
ability to read
coordinates and to
calculate using scales, such
as 1:50000.

Maths is Everywhere

History

Mathematics has its very own
history, from its roots in
ancient cultures, through the
Greeks and Romans (think
Pythagoras), onto Newton
and more recent history,
including tales of murder and
jealousy, culminating in the
20th century which has seen
mathematics form the bedrock
of modern society.

Maths is Everywhere

History

Graphs and charts provide
valuable insights when
analysing historical data.

Maths is Everywhere

Health and Social Care

Growth and physical
development in children has
been closely monitored, and
using statistics such as
percentiles we can accurately
track physical development
and use it as an indicator of
potential health problems.

Maths is Everywhere

Health and Social Care

Research into health and
social care, including
best practices, is often
conducted using surveys,
questionnaires, and
gathering of data, which
is then analysed and
presented using statistics
and graphs.

Maths is Everywhere

Languages 1+3=4 uno más tres es
8–2=6 cuatro
4 × 5 = 20 ocho menos dos es
10 ÷ 2 = 5 seis
cuatro multiplicado
por cinco es veinte
diez dividido por
dos es cinco

The Spanish mathematician Abraham
bar Hiyya was the first person to
record a method for solving
quadratic equations, during the 12th
century.

Maths is Everywhere

Languages

1+3=4 eins plus drei macht
8–2=6 vier
4 × 5 = 20 acht minus zwei
10 ÷ 2 = 5 macht sechs
vier mal fünf macht
zwanzig
zehn durch zwei
macht fünf

The German mathematician Carl
Friedrich Gauss, working in the early
19th century, is considered the Prince
of Mathematics, one of the greatest
mathematicians who has ever lived.

Maths is Everywhere

Languages

1+3=4 un plus trois fait
8–2=6 quatre
4 × 5 = 20 huit moins deux fait
10 ÷ 2 = 5 six
quatre fois cinque fait
vingt
dix divisé par deux
fait cinque

In the 17th century, the French
mathematician René Descartes created,
amongst other things, the coordinate
grid that we still use to draw graphs
today.

Maths is Everywhere

The Beauty of Maths

We don’t learn maths
because it can be applied
to other subjects, we learn
it because it exists, because
there is beauty in pattern
and number, and because it
is the language that
describes our world.

Maths is Everywhere

The Beauty of Maths

We don’t learn maths because it can be applied to other subjects, we
learn it because it exists, because there is beauty in pattern and number,
and because it is the language that describes our world.

Maths is Everywhere

Media Studies

So much animation
uses mathematics, from
Bézier curves to draw
moving grass, to
combinatorics to
design hundreds of
robots from just a few
component parts.

Maths is Everywhere

Media Studies

The equipment you use is
built upon mathematics.
Focus, aperture and
depth of field are all
related using calculations
of ratio and proportion.

Maths is Everywhere

Music

The tempo of a piece of music
determines how many beats
per minute (bpm) the music
runs at. Music software
calculates tempos in order to
speed up or slow down
recordings. Music technology
also uses the mathematics
behind sound waves, which
involves trigonometry
( , , ).

Maths is Everywhere

Music

semibreve minim crotchet quaver semiquaver
Length 1 ⁄ ⁄ ⁄ ⁄

A dot means the note is one-and-a-half times its usual length, so:
=+=

Maths is Everywhere

Music

By halving the length of a string, 
you double its resonant 
frequency and create an octave.  
So be it a piano, guitar, violin or 
any other stringed instrument, a 
note one octave higher will be 
created with a string exactly half 
the length.

Other notes are made by 
dividing the string into different 
fractions of its original length.

Maths is Everywhere

PD & RE

Percentages and figures are used to
consider how the world looks through
different eyes.

For instance:

• ¼ of the world’s population
identifies as Muslim.

• 112,330 households applied to
their local authority for
homelessness assistance in 2014.

• It is estimated that 2% of the UK
adult population is not
heterosexual.

Maths is Everywhere

Physical Education

Biomechanics is the
mathematical analysis of
physical performance,
impact, stresses and strains, in
order to improve sporting
ability and find ways of
minimising and treating injury.

Maths is Everywhere

Physical Education

Many athletes work to
improve their speed. By
measuring the time
taken to cover a
distance, you calculate
the speed using the
formula

speed = distance
time

Maths is Everywhere

Psychology & Sociology

Social scientists use advanced
statistical techniques, such as
hypothesis testing, to analyse
experiments and test their ideas.

Maths is Everywhere

Science

Biologists use mathematics to
analyse their experiments and to
model the world around us.

Without mathematics, our
understanding of the natural world
would be much more limited.

Mathematical modelling enables
biologists to predict everything
from population growth and decay
in species to how cells interact with
each other.

Maths is Everywhere

Science

Pharmaceuticals are created
using a lot of mathematics.
Firstly, quantities of each
ingredient are carefully
calculated, then the medicines
are tested on people and the
results of these tests analysed
using statistics, until the
pharmaceutical companies are
happy that the medicines are
both safe and effective.

Maths is Everywhere

Science Chemical reactions are modelled using
equations. For instance, the Arrhenius
Equation tells us how temperature
affects the rate of a reaction:

where is the reaction rate, is the pre-
exponential factor, is the activation energy,

is the universal gas constant and is the
absolute temperature (in Kelvin).

is an an irrational number, like , which
occurs in many equations that describe
exponential growth and decay.

Maths is Everywhere

Science

Any kind of data is often
best represented and
understood in a graph.
Since science involves lots
of observation and
gathering data, it
inevitably uses lots of
graphs!

Maths is Everywhere

Science

Projectile motion always forms the shape of a quadratic, and is modelled using quadratic equations.

Maths is Everywhere

Science

Using mathematical
equations, scientists know
how things move, how forces
affect motion, and can even
model the motion of liquids.

·0

Maths is Everywhere

Technology

Scale drawing is a
feature of technology,
and accuracy is
paramount to producing
quality work.

Maths is Everywhere

Technology 3D objects need to be
accurately represented
30˚ 30˚ in 2D drawings. One of
the most common ways
of doing this is through
isometric drawing (which
you normally do in
maths using dotty
paper).

Maths is Everywhere

Technology

Electrics and electronics
obey a number of
mathematical laws. For
instance, resistance in a
parallel circuit is
calculated using:

1 1⋯

Maths is Everywhere

Technology

Robotics makes regular use
of mathematics.
Trigonometry ( , , )
is used to create rotations
and movement of arms and
legs, as well as springing
and bouncing motion to
make movement smoother.

Maths is Everywhere

Textiles

Measuring, scale and proportion
skills are essential for working with
textiles.

Where you might estimate how much
more/less of a material you need to
make something bigger/smaller, in
the textiles industry, where wastage
costs money, these things need to be
calculated accurately.

Maths is Everywhere