mathematical hearts with Maple

by dr bob jantzen

2d and 3d mathematically described  heart shapes, realized here with the mathematical software Maple (computer algebra system: wiki).

3-d heart:

• heart.mw  heart in a box
  250MB when executed
• heartsmooth.mw 31MB saved image only, no code
• heartvolume.mw numerical approximation to volume as a percentage of the circumscribed rectangular box which holds it
• rotationanimation.mw how to do a 360 degree rotation of a 3d plot
   [animation: heartinaboxinmotion.gif]
  Heart in a box in motion with rough edges...
    [and don't all real hearts have rough edges, metaphorically speaking?]
  
• https://love.imaginary.org/ [2 parameter heart redrawing, rotatable view with mouse]
  hmm, very efficient graphic [from this NYTimes article]
  [(x^2+((1+b)*y)^2+z^2-1)^3-x^2*z^3-a*y^2*z^3=0, 2 parameter family to play with]
  

The lace heart:

• lace valentine! thanks, john!
  This is the polar coordinate graph of the following equation:
  
• Tweeking this last heart gives a symmetric version: heartlacetweek.mw
  Notice the imperfection at the bottom of the heart! It reveals the asymmetry about the vertical reflection axis of symmetry and an irregularity at the tip in the smoothness of the plot. Fixing these reveals the power of a computer algebra system.
  
  
• some more d2 hearts from Wolfram MathWorld

heart animation from Physicist TV:

• heartanimation.mw