# 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

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