Morphing Circles

Hard
Have you ever wondered what would happen if you added a sine function to a circle? In this project, you'll find out! You'll graph a regular circle and then add a sine function to it. You'll then observe the pattern created by the bumps that form on the circle.

Hypothesis

The hypothesis is that adding a sine function to a circle will create a pattern according to how the circle "bumps" around the curve.

Method & Materials

You will graph a regular circle and then add a sine function to it. You will then record the number of bumps you see as you increase the period of the sine function.
You will need a computer with the software "Nucalc" and a way to record your data.

Results

This project shows that when a sine function is added to a circle, the number of bumps is always an odd number. The number of bumps is equal to the number of times the sine curve crosses the x-axis while inside the original circle.

Why do this project?

This science project is unique because it shows how a sine function can be used to create a pattern on a circle.

Also Consider

Experiment variations to consider include using different radii for the circles and using ellipses instead of circles.

Full project details

You can find additional information and details for this science fair project here. Have fun exploring!
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