How to Put Pacman on Graphing Calculator

Displaying Pac-Man on a graphing calculator can be a fun way to explore parametric equations and trigonometric functions. This guide provides step-by-step instructions for creating a Pac-Man animation using your calculator's graphing capabilities.

Introduction

Graphing calculators are powerful tools that can go beyond simple graphing. By understanding parametric equations and trigonometric functions, you can create animations like Pac-Man. This technique works on most graphing calculators that support parametric mode, including TI-84, TI-83, and Casio models.

Note: The exact steps may vary slightly depending on your calculator model. Refer to your device's manual for specific instructions.

Basic Steps

Step 1: Set Up Parametric Mode

First, ensure your calculator is in parametric mode. This is typically found under the MODE menu. Select Parametric and set the start and end values for your parameter (usually t) to 0 and 2π (approximately 6.28) for a full circle.

Step 2: Define the Pac-Man Body

For the main body of Pac-Man, you'll use a semicircle. Enter the following equations:

X1T = 2 + 2cos(t)

Y1T = 2 + 2sin(t)

This creates a circle centered at (2, 2) with radius 2. The parameter t ranges from 0 to π (approximately 3.14) to create a semicircle.

Step 3: Add the Pac-Man Mouth

To create the mouth, you'll use another parametric equation. Add these equations:

X2T = 2 + 2cos(t)

Y2T = 2 + 2sin(t)

Set the parameter range for this equation to 0 to π/2 (approximately 1.57) to create a quarter-circle mouth.

Step 4: Graph and Adjust

Graph the equations and adjust the window settings to ensure the entire Pac-Man is visible. You may need to adjust the Xmin, Xmax, Ymin, and Ymax values in the WINDOW menu.

Advanced Techniques

Creating Animation

To make Pac-Man move, you can use the calculator's animation feature. Set the parameter to animate by going to the DRAW menu and selecting Animate. Adjust the speed and direction as desired.

Adding Ghosts

You can extend this project by adding ghosts. Use similar parametric equations but with different colors and positions. For example:

X3T = 4 + cos(t)

Y3T = 4 + sin(t)

This creates a smaller ghost circle centered at (4, 4).

Changing Colors

Most graphing calculators allow you to change the color of each graph. Use the STYLE menu to select different colors for Pac-Man and the ghosts.

Troubleshooting

Pac-Man Doesn't Appear

If Pac-Man doesn't appear on the graph, check that:

You're in parametric mode
The parameter range is set correctly (0 to π for the body, 0 to π/2 for the mouth)
The window settings are appropriate for the size of your shapes

Animation Doesn't Work

If the animation feature isn't working, try:

Restarting your calculator
Checking that the animation is enabled in the DRAW menu
Ensuring you have enough battery power

Graph Looks Distorted

If the graph looks distorted, adjust the window settings to ensure equal scaling on both axes. You may need to set Xscl and Yscl to the same value.

FAQ

Can I use this technique on any graphing calculator?: This technique works on most graphing calculators that support parametric mode, including TI-84, TI-83, and Casio models. However, the exact steps may vary slightly depending on your model.
How can I make Pac-Man move faster or slower?: To adjust the animation speed, go to the DRAW menu and select Animate. You can then adjust the speed using the calculator's controls.
Can I add more characters to the animation?: Yes, you can add additional characters by creating more parametric equations with different positions and colors. Just make sure to keep the parameter ranges appropriate for each shape.
Is there a way to save my Pac-Man animation?: Most graphing calculators allow you to save your work, but the exact method depends on your model. Typically, you can save the current state of the calculator or transfer the equations to a computer.
Can I use this technique to create other animations?: Absolutely! The parametric equations technique can be used to create many different types of animations, from simple shapes to complex scenes.