Valentines’ Day

14th February is coming up!  Here is a great exercise in understanding the modulus function and the equation of a circle.

y = |x| ± √(4 – x²)

You can copy this text and paste it into Autograph (Autograph understands Unicode mathematics symbols!) First discuss what the two elements represent:
y = |x|   and   y = ± √(4 – x²)

Later on, edit the equation (double-click on the graph) , and replace ‘4’ with ‘r²’ and set ‘r’ to be 2, so nothing is changed.  Now you can now use the constant controller to set the value of ‘r’ animating from 1.8 to 2.2 in steps of 0.05 … Enjoy!
(Boom-di-di-boom-di-di-boom-di-di-boom …)

Download 2D Autograph file (.agg) [open constant controller]
Download 3D Autograph file (.agg) [open constant controller]

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