Happy Valentine's Day Plot: x,y = 16sin^3 t, 13cos t-5cos2t-2cos3t-cos4t

  • Context: Undergrad 
  • Thread starter Thread starter Simon Bridge
  • Start date Start date
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Discussion Overview

The discussion revolves around a mathematical plot representing a heart shape defined by the parametric equations \(x = 16\sin^3 t\) and \(y = 13\cos t - 5\cos 2t - 2\cos 3t - \cos 4t\). Participants share their thoughts on the aesthetic and mathematical aspects of the plot, as well as explore related mathematical concepts.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant presents the parametric equations for the heart shape plot.
  • Another participant expresses interest in finding a transfer function with a Nyquist plot that resembles the heart shape.
  • Several participants compliment the heart shape and share Valentine's Day greetings.
  • A participant notes the purity of the equation form used to create the plot.
  • Another participant mentions a variation of the original plot, suggesting a Spirograph-like appearance based on the same formula.

Areas of Agreement / Disagreement

Participants generally agree on the aesthetic appeal of the heart plot and share positive sentiments about it. However, there are no explicit agreements or disagreements regarding the mathematical properties or implications of the equations presented.

Contextual Notes

Some discussions involve variations on the original plot, but the mathematical details and assumptions behind these variations remain unspecified.

Who May Find This Useful

Individuals interested in mathematical plots, parametric equations, and those celebrating Valentine's Day with a mathematical twist may find this discussion engaging.

Simon Bridge
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Plot[tex](x,y)=\left ( 16\sin^3 t\;\; ,\;\; 13\cos t - 5\cos 2t -2\cos 3t -cos 4t \right )[/tex]:)
 
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nice, let me see if I can find a transfer function with nyquist plot similar to this.

e05a28ecda266f1ae662146ec07adc0c1f463cf72782a2f4ff0afe468fd404495g.jpg
 
Nice heart! Happy Valentine's Day!
 
TO: Evo
[/color]FROM: Astronuc

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Happy Valentine's Day!​
 
Though the equation form is so pure...
 
Evo said:
Nice heart! Happy Valentine's Day!
Only stay home or let's with friends.
 
Variation on a theme. Still based on the formula posted by Simon, but with a Spirograph like look.
 

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