Seeing Math Patterns in Nature

Seeing
Math
Pa,erns
in
Nature
Mary
Van
Dyke
Green
STEM
Learning
NSTA
Conference
Richmond,
VA
October
2014

• Pack
n’
Grow
• Pinecones
Overview
and
Pineapples
• Sunflowers
and
Daisies
• Fibonacci
and
non-‐Fibonacci
• Phyllotaxis
and
Branching
• Squares
and
Spirals
• Make
Your
Own
Series
• Resources

Pack
n’
Grow
Hexagonal
Pack
• Maximum
strength
with
minimum
materials
Square
Pack
LaUces

h,p://goo.gl/56hbKU
How
Many
Spirals?

Leonardo
of
Pisa
–
son
of
Bonacci
Liber
Abaci
1202
c.
1170
–
c.
1250
Who
Was
Fibonacci?

0,
1,
1,
2,
3,
5,
8,
13,
21,
34,
55,
89,
144,
…
F
n
=
F
n-‐1
+
F
n-‐2
where
F
0
=
0
and
F
1
=
1
0
+
1
=
1
1
+
1
=
2
1
+
2
=
3
2
+
3
=
5
3
+
5
=
8
5
+
8
=
13
8
+
13
=
21
Math
–
The
Fibonacci
Series

h,p://goo.gl/aUwknV
How
Many
Spirals?

90%
of
Plants
Grow
in
Fibonacci
Pa,ern

1000
seeds
1000
seeds
3000
seeds
Efficiency
-‐
Sunflower
Spiral
Pa,erns

• Wolfram
Mathemajca
-‐
Interacjve
models
• Vi
Hart
-‐
Doodling
in
Math:
Spirals,
Fibonacci,
and
Being
a
Plant
,
3
parts
on
YouTube
Pa,erns
and
Dynamic
Models

Wolfram
Mathemajca
Demonstrajons
Search
“phyllotaxis”
for
about
a
dozen
models
h,p://demonstrajons.wolfram.com/search.html?query=phyllotaxis
Phyllotaxis
Spirals
in
3D
h,p://demonstrajons.wolfram.com/
PhyllotaxisSpiralsIn3D/
Interacjve
Tools
On
the
Fundamental
Theory
of
Phyllotaxis
OnTheFundamentalTheoremOfPhyllotaxis
Fibonacci
Tree
FibonacciTree/

Alan
Turing’s
Sunflowers
Global
Experiment
2012
Big
Data
–
Cijzen
Science

Roast
In-‐Shell
Sunflower
Seeds
Brush
or
pick
seeds
off
seedhead
Soak
and
Salt
• Cover
unshelled
seeds
with
salt
water
(
¼
to
½
cup
of
salt
per
two
quarts
of
water
• Soak
overnight
• Drain
off
water,
pat
seeds
dry
(Or:
Skip
saljng
and
soaking
and
roast
unsalted)
Roast
• Preheat
oven
to
300
º
F
• Spread
seeds
evenly
on
baking
sheet
• Bake
for
30
–
40
minutes
• Check
and
sjr
occasionally
• Cool
before
eajng
• Store
when
cool
in
airjght
container
Roast
Sunflower
Seeds

Fibonacci
and
non-‐Fibonacci
Series

Leaf
Arrangement
-‐
Phyllotaxis

Phyllotacjc
Architecture
2012

The
Pineapple,
The
Core
and
The
Gherkin…

Think
of
a
number…
Make
Your
Own
Series

Think
of
a
number…
2. Decide
a
second
number
3. Add
the
two
together
Make
Your
Own
Series

Think
of
a
number…
2. Decide
a
second
number
3. Add
the
two
together
4. Determine
the
next
12
numbers
in
your
sequence
Make
Your
Own
Series

Think
of
a
number…
2. Decide
a
second
number
3. Add
the
two
together
4. Determine
the
next
12
numbers
in
your
sequence
5. Name
your
series
of
numbers
Make
Your
Own
Series

Think
of
a
number…
2. Decide
a
second
number
3. Add
the
two
together
4. Determine
the
next
12
numbers
in
your
sequence
5. Name
your
series
of
numbers
6. What
are
the
ra4os
of
each
of
your
consecujve
numbers
divided
by
the
next
larger
number
in
the
sequence?
7. What
are
your
conclusions
about
the
ra4o
of
consecujve
numbers
in
your
sequence
–
as
numbers
get
larger?
Make
Your
Own
Series

• Fibonacci-‐style
Take
Homes
math
sequences
are
prevalent
in
nature
and
design
• 90%
of
plant
species
grow
in
a
Fibonacci
way
• Why?
Efficiency
for
growth,
leaf
arrangement,
branching,
flower
and
seed
arrangement
• Correlajons
with
Fibonacci-‐style
sequences
include
breeding
pa,erns
and
sound/music
• You
can
study
these
pa,erns
at
all
grade
levels
with
STEM
integrated
projects
with
art
and
design
components

Seeing
Math
Pa,erns
in
Nature
Projects:
• Ask
and
Define
Problems
• Plan
and
Carry
Out
Invesjgajons
• Analyze
and
Interpret
Data
• Develop
and
Use
Models
• Construct
Explanajons
and
Design
Solujons
• Engage
in
Evidence-‐based
Argumentajon
• Use
Math
and
Computajonal
Thinking
• Obtain,
Evaluate,
and
Communicate
Informajon
NGSS
–
Hit
the
Standards

h,p://goo.gl/HvvLdO
Credits
and
Resources
Thank
You!

Contact
me:
Mary
Van
Dyke
Green
STEM
Learning
maryvandyke4@gmail.com

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