Art Project

 A dream catcher is a decorative piece originates from the indigenous people. It is meant to filter out the bad dreams and capture the good dreams for the sleeper. The circular shape of the dreamcatcher symbolises the belief of life is circular. The web in the circle helps catch the good dreams and transcend down to the sleeper through the feathers. 

 

The Mathematical idea involves here is the Pisano period. Pisano period is formed by dividing the Fibonacci sequence by any number “n” and only focus on the remainder (Modular Arithmetic). These remainders repeat after a certain number of terms.

 

Example:

Fibonacci Sequence

1

1

2

3

5

8

13

21

34

55

89

144

233

377

610

987

Remainder after dividing by 3

1

1

2

0

2

2

1

0

1

1

2

0

2

2

1

0

Remainder after dividing by 4

1

1

2

3

1

0

1

1

2

3

1

0

1

1

2

3

 

Referring to the table above, when each term of the Fibonacci sequence is divided by 3, the remainder forms a repeating pattern with length 8 (1,1,2,0,2,2,1,0). Similarly, a repeating pattern of length 6 is formed when divided by 4 (1,1,2,3,1,0). 

 


If we were to place these remainders evenly on a circle, we can trace the order of the period by joining the associated point. Shown below is the trace of the repeating remainder when dividing the Fibonacci sequence by 4 (1,1,2,3,1,0). This pattern forms the web of the dreamcatcher I created. The periodic nature of the Pisano period also echoes the belief of life is circular. Moreover, the number of feathers in this art piece represents the number we use to divide the Fibonacci sequence. 








Reference:



1.     Weisstein, E. W. (2003). Pisano Period. https://mathworld. wolfram. com/.

 

2.     https://www.theindigenousfoundation.org/articles/dreamcatchers

 

3.     The So-called Fibonacci and Medieval Numbers India in Ancient

Singh, P. (1985). The so-called Fibonacci numbers in ancient and medieval India. Historia Mathematica, 12(3), 229-244.

 

4.     Fibonacci Sequence : History and Modern Applications, in: History and Development of Mathematics in India

History and Development of Mathematics in India (pp.155-180), Edition: 2022, Publisher: National Mission for Manuscripts and DK Printworld, New Delhi

 

5.     On the Origin of the Fibonacci sequence

Scott, T. C., & Marketos, P. (2014). On the origin of the Fibonacci Sequence. MacTutor History of Mathematics, 23.





















Comments

  1. Amanda FritzlanDecember 20, 2022 at 11:24 AM

    Duncan, Thank you for sharing your exploration of the intriguing Pisano period. I like how you played with representing the Pisano period through circular constructions with a hoop and string. I appreciated how the practical considerations and aesthetics informed your choice of which one to present. You began with the idea of an Indigenous dream catcher and related geometries and sequences. I have made dreamcatchers with an Indigenous artist and support worker in a school-based workshop. I had not thought of the mathematics in creating them.

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