How to: Equation Butterfly on a Graphing Calculator

Written by paul bragulla
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How to: Equation Butterfly on a Graphing Calculator
A simple image of a butterfly can be produced with many graphing calculators. (Design Pics/Valueline/Getty Images)

Graphing calculators such as the TI series from Texas Instruments can graph various functions with the resultant plot appearing on the screen. Graphing calculator art uses a series of overlayed plots to create an image, with each function contributing one line to the picture. A butterfly, one of the simplest examples, can be made using the graphing function of any TI series calculator.

Skill level:
Moderately Easy


  1. 1

    Press the "Mode" button on the front of your TI-series graphing calculator. It should be the second button from the left on the second row of buttons from the top (including the row of buttons just under the screen).

  2. 2

    Select "Pol" on the menu that appears by moving the cursor over it with the direction arrow buttons. It should be on the fourth line from the top. Press "Enter" when the cursor is over it to select it. "Pol" is an abbreviation for "polynomial," the function you'll need to enter to create the butterfly image.

  3. 3

    Press the "Y=" button on the calculator in the top left of the panel, immediately below the screen. The screen that comes up should have a column consisting of "R1=," "R2=," R3=," etc. on the left side of the screen. The cursor should be blinking in the space immediately after "R1=," prompting you to enter the formula. The butterfly picture requires only one formula, but if you were making an image that required two or more plots to be overlayed, each of these "R's" would have a formula in the form of "y=..." after it, with the "R" representing the "y."

  4. 4

    Press the "-" button on the keypad to enter a negative sign, then type the number "10." Press the "sin(," "cos(," and "tan(" buttons, then press the variable button (the one with an "X," "T," "theta" and an "n" on it). Finish by closing the parentheses with the right-parenthesis button. Press "Graph" (the top right button on the keypad) and the butterfly image should appear.

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