Heart to Bell Demonstration

Plot the family of polar curves r(t)=cos(5t)+a cos(t) for a = -5, -4, ... , 4, 5.

Heart to Bell Family with stepsize = 1

This demonstration is used to motivate student interest in learning polar coordinates.

Reference: Michael W. Chamberlain, U.S. Naval Academy, Annapolis, MD, "Heart to Bell", The College Mathematics Journal, Vol. 25, No. 1, January 1994.

How To Make a QuickTime Movie of the Heart to Bell Demonstration

You will need the "Pro" version of the QuickTime Player ($30.00) which can be downloaded from www.apple.com.

A. First we need to create a sequence of pictures for the movie.

Create an empty folder called "Heart to Bell Folder" on your desk top.
Select the cell containing the constant "a" in the Work window.
Change the step size from 1 to 0.5.
Select and plot the r(t) function.

A sequence of 21 polar curves will be plotted which change from a Heart shape to a Bell shape.

Click in the Graph window to make it active.
Select Export - Graph from the File Menu.

A window will open that will allow you to save the plot of each curve as a picture.

Use the scrolling list to navigate to the "Heart to Bell Folder" on your desktop.
Delete "Graph" from the window's edit field and enter "HeartBellPict".
Click in the Animation Sequence check box so that it becomes checked.
Click the Save button.

First, all 21 curves will be replotted using the first curve's color and they will be saved as a sequence of picture files with the names:

HeartBellPict 01, HeartBellPict 02, ..., HeartBellPict 21.

Next, the message "A sequence of 21 pictures were saved." will be written in the Report window. Finally, the curves will be replotted in color.

B. Next, we use QuickTime Player Pro to generate a movie.

Start the QuickTime Player Pro Application by double-clicking its icon.
Select Open Image Sequence... from the File menu.

A window will open that will let you import the sequence of Heart to Bell pictures.
Use the scrolling list and buttons to navigate to the pictures in the Heart to Bell Folder on the desktop and click the Open button.

The window will close and the Image Sequence Settings window will open.
Accept the default frame rate of 15 frames/sec and click the OK button.

The window will close, a new window will briefly appear showing the progress of generating the movie, and finally the first frame of the movie will be displayed by QuickTime Player Pro.
Save the movie by selecting Save As... from the File menu.
A window will open that will allow you to save the movie.
Accept the "Save Normally" default, enter "HeartToBell.mov " in the edit field as the
movie's name, and
Click the OK button.

The movie will be saved in the file "HeartToBell.mov".
To play the movie, click the large round button containing an arrow at the bottom of the QuickTime Player.
To play the movie over and over, select either Loop or Loop Back and Forth from the Movie menu.

How To Make a GIF Animation of the Heart to Bell Demonstration

You will need the shareware program "GraphicConverter" ($35.00) which can be downloaded from www.lemkesoft.com.

If you have not done so, complete the steps of (A) above.

The following steps are needed to configure the GraphicConverter to generate an animation using the GIF format.

Start the GraphicConverter application.
Select Convert More... (Convert... in version 3.9.1) from the File menu.

A window will open that will let you convert the pictures to an animation in the GIF format.
Click on the Dest. Format pop-up menu on the RIGHT side of the window and scroll to "GIF" and select it.
Click on the Options button on the RIGHT side of the window.
A window will open letting you set the GIF animation options.
Click in the Create Movie check box and in the Loop check box so that both are checked. Also, make sure that the 89a radio button is selected.
Enter 100 into the "Delay" edit field.
Click the OK button to close the Options window.
Now, we need to set the source to be the folder containing the pictures.
Click on the Filter pop-up menu on the LEFT side of the window and scroll to "PICT" and select it.
Use the scrolling list on the LEFT to again locate the "Heart to Bell Folder " on the desk top and select it. Be sure not to open the folder!
Next, click the Convert button at the top center of the window.

The sequence of pictures in the folder will be converted to an animation in GIF format and saved inside a nested folder with the name "HeartBellPict 01.gif".
Finally, locate the "HeartBellPict 01.gif" animation and change its name to HeartToBellAnimation.gif.
You can show the movie using GraphicConverter but the QuickTime player is better.
You can also show it by dragging its icon on top of a web browser such as Netscape.

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