Applied MathsMaths in the real world

Pure maths vs. Applied maths

Pure maths: Axioms Theorems

Applied maths: What you know What is used in other disciplines

Applied Maths - the universal toolbox

Reality makes sense

Maths makes sense

Reality is mathematical

The truth is out there...Maths in nature

Maths & aesthetics

Fibonacci of PisaFibonacci’s sequence:

1, 1, 2, 3, 5, 8, 13, 21...

Constructed by the addition of pairs of numbers within the sequence.

You know this sequence like...

A flower by any other number...

Calla

Lily

Euph

orbi

a

Trilli

um

Conv

olvu

lus

Blac

k-ey

ed S

usan

Wat

er L

ily

Twist and count...

Succulent Spirals:

How many spirals make up the pattern?

Counting Cones...

Can you count them?

Anti-clockwise:34.Clockwise:55

Magic, Maths, or Mysterious Coincidence

These organic patterns have been explained in terms of ‘packing’, where the greatest number of similar shapes can be fitted into the least space.

Nature is an incessant whittler of inefficiency, and the most frugal user of its resources will be the one most likely to survive lean times, reproduce, and succeed.

Molecular MathsAt a molecular level Fibonacci spirals arise spontaneously in mutually repulsive silicon dioxide particles on a silver core.

Differing amounts of stress placed on the microstructures lead to different Fibonacci spirals.

Building beauty.This forms a very special shape – the Golden Section.

The Golden Section or Golden ratio is said to be a natural shape that appears in nature, and art & architecture from around the world.

Perfect Parthenon.

Mayan Masonry

Golden Ratio Spirals in nature

Snail shells form a spiral of growth in the same ratio

As do some climbing plants

Art through the ages

ActivitiesNature: Measuring shells

Counting leaves

Art: Perspective calculation(Alberti’s Algebra)The Brunelleschi

method