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Geometric Patterns
in Nature
IS THIS BY CHANCE?
What makes snowflakes so
beautiful?
Why did God do this?
How does a
tree point to
infinity?
What makes the Eiffel tower so beautiful and
recognisable?
What was considered in the design?
Where did man get this talent for creative art?
What makes Big Ben in
London so beautiful and
recognisable?
What was considered in
the design?
Where did man get this
talent for creative art?
Fractals
Breath
Trailer
Lungs
Breathing
The very
essence of life!
Chat
Draw some lungs!
The bronchi branch into smaller bronchi and
then even smaller bronchioles.
These tiny tubes stretch out into every part of
your lungs. Some, only the thickness of a hair.
About 30,000 bronchioles in each lung.
Each bronchiole tube ends with a cluster of
small air sacs called alveoli (about 600 million)
for air to pass through
Bronchial Tree
The volume of a pair of human
lungs is only ~4 - 6 litres
however
The surface area is between 50
and 100 square meters.
That's about the same area as a
tennis court!
I praise you because of the wonderful
way you created me.
Everything you do is marvelous!
Of this I have no doubt.
Psalm 139:14 CEV
Where else might
you come across
fractals in nature?
Fractals
Chat
What does the movie “Up” have
in common with the Sierpinski
Triangle?
Humans have take the patterns
which God built into nature and
used these to create other
ideas.
Both based on fractals!
“When I consider your heavens, the work of your fingers, the
moon and the stars, which you have set in place, what is
mankind that you are mindful of them, human beings that you
care for them?” Psalm 8:3-4
Geometric
design – built
into creation –
which leads us
to the worship
God the creator

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Year 9 Geometric patterns in nature.pptx

  • 2. What makes snowflakes so beautiful? Why did God do this?
  • 3. How does a tree point to infinity?
  • 4. What makes the Eiffel tower so beautiful and recognisable? What was considered in the design? Where did man get this talent for creative art?
  • 5. What makes Big Ben in London so beautiful and recognisable? What was considered in the design? Where did man get this talent for creative art?
  • 7.
  • 11.
  • 12. The bronchi branch into smaller bronchi and then even smaller bronchioles. These tiny tubes stretch out into every part of your lungs. Some, only the thickness of a hair. About 30,000 bronchioles in each lung. Each bronchiole tube ends with a cluster of small air sacs called alveoli (about 600 million) for air to pass through Bronchial Tree
  • 13. The volume of a pair of human lungs is only ~4 - 6 litres however The surface area is between 50 and 100 square meters. That's about the same area as a tennis court!
  • 14. I praise you because of the wonderful way you created me. Everything you do is marvelous! Of this I have no doubt. Psalm 139:14 CEV
  • 15. Where else might you come across fractals in nature? Fractals Chat
  • 16.
  • 17. What does the movie “Up” have in common with the Sierpinski Triangle?
  • 18. Humans have take the patterns which God built into nature and used these to create other ideas. Both based on fractals!
  • 19. “When I consider your heavens, the work of your fingers, the moon and the stars, which you have set in place, what is mankind that you are mindful of them, human beings that you care for them?” Psalm 8:3-4
  • 20. Geometric design – built into creation – which leads us to the worship God the creator

Editor's Notes

  1. Burden, A. Symmetry, harmony, pleasing to the eye.
  2. Kummur, A. Fractals – in ‘perfect’ conditions, with ‘unlimited growth’!
  3. Yanase M Delanoix A Gan C
  4. Be, H. Clever visuals
  5. Photo: https://www.newsweek.com/how-does-iron-lung-work-polio-survivor-last-us-1083104 Have this slide open when students arrive Sit with this slide open for a while. Tease out ideas such as: I wonder who this person is? “I wonder what their life would be like”? Share knowledge and stories of lung machines. Draw out the importance of lungs. Intended as a hook to draw participants into the presentation; causing them to wonder where this is going; create interest to find out
  6. Show clip Lungs – part of God’s design for the most basic function of ‘life’ in our human bodies (another ‘attention grabber’ to consider this idea)
  7. Thoughts that come to mind when you see this slide? What do you notice? What do your feel? What do you want to do? COVID has highlighted this amazing organ. We take for granted – the very breath of life. Almost desensitised to photos like this at the moment.
  8. On the first page: have a go at drawing lungs. Hopefully someone will include the idea of ‘trees branching’ – draw attention to this idea. If no one seems to be including this – quietly suggest the idea into the discussion that’s happening while everyone is drawing. The intent is to have active participation, and not give room for passive participation, yet in a safe and accessible environment. The alternative to this activity would be to have someone come up and draw lungs on the board – however this allows ‘students’ to remain passive. Invite everyone to share (hold them up together – or go around and explain). In a classroom you might invite ‘feedback’ and give time for improvement on drawings.   Photos: (L. Clarkson, 2019)  
  9. One depiction of lungs
  10. The brain; veins; trees; snowflakes; broccoli… How are these the same? How are they different?
  11. Photo: Ryan Searle
  12. Photo: (R. Watson, 2019)
  13. Some interesting things to consider: ideas from: https://fractalfoundation.org/OFC/OFC-index.htm
  14. Humans have taken the patterns which God built into nature and used these to create other ideas! Pixar Animation studios
  15. Humans have taken the patterns which God built into nature and used these to create other ideas! Pixar Animation studios
  16. Fractals: indices; infinity; growth; logarithms; proportion; similarity; geometry; surface area and volume; dimensions; optimisation; computer graphics; design etc. One key idea is that fractals point to the infinity of the creator God “Mathematics through the eyes of faith” (Bradley & Howell, 2011) has some interesting discussions and applications The Code: Shapes chapter 4 (Childs, 2009) contains some beautiful examples You could then continue with examples of how humans, made in God’s image, have taken the ideas of fractals to create other ideas, particularly art and design: have students spend 10 mins finding their favourite image that incorporates fractals; add a Bible verse or ‘speech bubble’; print them and hang them in the classroom An exemplar activity/ assignment will be distributed either as a handout or as a downloadable link to take home (Appendix 1) Photo: Lu