Applied Maths
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Transcript of Applied Maths
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Applied MathsMaths in the real world
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Pure maths vs. Applied maths
Pure maths: Axioms Theorems
Applied maths: What you know What is used in other disciplines
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Applied Maths - the universal toolbox
Reality makes sense
Maths makes sense
Reality is mathematical
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The truth is out there...Maths in nature
Maths & aesthetics
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Fibonacci of PisaFibonacci’s sequence:
1, 1, 2, 3, 5, 8, 13, 21...
Constructed by the addition of pairs of numbers within the sequence.
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You know this sequence like...
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A flower by any other number...
Calla
Lily
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Euph
orbi
a
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Trilli
um
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Conv
olvu
lus
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Blac
k-ey
ed S
usan
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Wat
er L
ily
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Twist and count...
Succulent Spirals:
How many spirals make up the pattern?
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Counting Cones...
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Can you count them?
Anti-clockwise:34.Clockwise:55
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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.
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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.
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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.
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Perfect Parthenon.
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Mayan Masonry
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Golden Ratio Spirals in nature
Snail shells form a spiral of growth in the same ratio
As do some climbing plants
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Art through the ages
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ActivitiesNature: Measuring shells
Counting leaves
Art: Perspective calculation(Alberti’s Algebra)The Brunelleschi
method