Spirolaterals Math Is Art

The Objective

The purpose of this experiment is to find number patterns in spirolaterals.

Methods/Materials

Although spirolaterals can be drawn by hand using a ruler and protractor, it is tedious, time consuming, and error prone.

Instead a computer program was used to drawn spirolaterals using the following variables: X = line length b = turning angle Z = number of turns R = number of repetitions.

Results

The following patterns were observed:

1) If b * Z = 360 the spirolateral will not close.

2) The number of repetitions to close a spirolateral is 360/ b * z if b * Z equals a factor of 360.

3) Spirolaterals with turning angle values of b and 360 - b will look the same, just flipped.

Conclusions/Discussion

My original hypothesis was that if b was a factor of 360, the spirolateral would be closed because there are 360 degrees in a circle. Having b be a factor of 360 does not make it closed, but rather when b * Z = 360 the spirolateral was not closed. It is possible to predict how many repetitions it will take to close a spirolateral: R = b * Z/360. However, it is only true when b * Z is a factor of 360. Spirolaterals with turning angle values of b and 360 - b will look the same, just flipped. This is because b is the inner angle and 360 - b is the outer angle. An example of this is when b = 144 and b = 216 (360 - 144 = 216).

The purpose of this experiment is to find number patterns in spirolaterals.

Science Fair Project done By Jennie Werner

 

 

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