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

  • Thread starter Simon Bridge
  • Start date
In summary, the conversation revolved around a mathematical equation for a heart shape and variations based on it. The equation was expressed in polar coordinates and was inspired by Valentine's Day. There was also discussion about staying home or being with friends.
  • #1
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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  • #2
nice, let me see if I can find a transfer function with nyquist plot similar to this.

e05a28ecda266f1ae662146ec07adc0c1f463cf72782a2f4ff0afe468fd404495g.jpg
 
  • #3
Nice heart! Happy Valentine's Day!
 
  • #4
TO: Evo
FROM: Astronuc

MXXOO-----MXXOO
MXXXXXOO---MXXXXXOO
MXXXXXXXXOO-MXXXXXXXXOO
MXXXXXXXXXXXXXXXXXXXXXXOO
MXXXXXXXXXXXXXXXXXXXXXXXXO
MXXXXXXXXXXXXXXXXXXXXXXX
MXXXXXXXXXXXXXXXXXXXXX
MXXXXXXXXXXXXXXXX
MXXXXXXXXXXXX
MXXXXXXXX
MXXXX
MXX
M

Happy Valentine's Day!​
 
  • #5
Though the equation form is so pure...
 
  • #6
Evo said:
Nice heart! Happy Valentine's Day!
Only stay home or let's with friends.
 
  • #8
Variation on a theme. Still based on the formula posted by Simon, but with a Spirograph like look.
 

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1. What is the significance of the x,y plot in the equation for "Happy Valentine's Day"?

The x,y plot in the equation represents the shape of a heart. The equation is a parametric equation that describes the motion of a point on a heart-shaped curve as t (time) varies.

2. How does the equation create the heart shape?

The equation uses trigonometric functions, specifically sine and cosine, to create the heart shape. The term 16sin^3 t creates the top half of the heart, while the terms 13cos t-5cos2t-2cos3t-cos4t create the bottom half.

3. Why is the equation called "Happy Valentine's Day"?

The equation is called "Happy Valentine's Day" because the heart shape it creates is commonly associated with love and Valentine's Day. Additionally, the equation was likely named as a clever play on words, using the initials of the variables (x and y) to spell "xy", another way of writing "love".

4. Can the equation be used to create other shapes?

Yes, the equation can be modified to create other shapes by changing the coefficients and/or adding more trigonometric terms. However, the resulting shape may not resemble a heart or have the same symbolic meaning.

5. What is the practical application of this equation?

The equation has no practical application in science or mathematics, but it can be used for artistic purposes, such as creating heart-shaped graphics or animations. It is also a fun way to celebrate Valentine's Day and spread love and happiness.

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