Wednesday, August 13, 2014

Mathematical equations of love, heart, penis and the boomerang


Love is complicated. But the mathematics of it is very simple:
  - It starts with "I love you" where "I love" is a constant, and "you" is a variable.
  - Later on, it is:  1 + 1 = 1
  - And later still:  1 + 1 >= 3
Any questions?

Now, let us explore the mechanics of love.


Love comes from the heart. The mathematical equation of the heart is:

        To see the above graph, go to WolframAlpha website
        At the input area, type in:
            (y - 0.75|x|)^2 + (0.75x)^2 = 1
        And you'll see the heart curve.

You get a slightly different shape of the heart by changing the value of 0.75. Have a try at 0.6 or 0.9 or other values. I find 0.75 more aethetically pleasing.

Actually, it just strikes me that the following parametrised equation
            (y - a|x|^b)^2 + (cx)^2 = d

(where you can set the values of the parameters  a, b, c and d)
can draw just about any heart shaped curve that one can imagine (and more) ... I'm claiming this parametrised equation as Paul Ma's Heart Equation.

So far, no one has disputed my claim in the math.stackexchange forum:

By setting  a=0.75,  b=1,  c=0.75  d=1  into Paul's Heart Equation, it becomes the previously mentioned heart curve.

If you set  a=1,  b=0.5,  c=1  d=4,  you'll produce:
    (y - |x|^0.5)^2 + x^2 = 4
Type the above into the WolframAlpha input area and you'll see that its heart is pretty good looking too:

How about you have a go at various other values of the parameters  a, b, c, d?  Examples are:
    a=0.5,  b=0.5,  c=0.7  d=0.5
    a=0.6,  b=(2/3),  c=0.8  d=0.9

If you discover other good sets of values to use, I would be interested to hear from you.


Now, when you give out love, love always comes back to you. Hence you expect the mathematical equation of a boomerang to be similar to that of a heart, right?  Indeed it is.  Set  a=0.5,  b=1,  c=0.13,  d=1  in Paul's Heart Equation to produce:
    (y - 0.5|x|)^2 + (0.13x)^2 = 1
Type the above into WolframAlpha and you'll get

Does love make the world go round?

Well, the heart certainly makes the world go round. Take a look at Paul's Heart Equation again:

Let  a=0, b=any, c=1, d=1  and it becomes a perfect circle !
    y^2 + x^2 = 1

But in a real world nothing is ever so perfect.  There are always pits and bumps.
Set  a=1, b=0.5, c=1, d=500  and you'll get:
    (y - |x|^0.5)^2 + x^2 = 500


Of course, you can't talk about love without mentioning the penis. The mathematical equation of a penis is:
    y = |sin(x)| + 5*exp(-x^100)*cos(x)  from -3 to 3
Type the above into WolframAlpha to produce

The Bum

This is covered in my blog From Golden Ratio to golden arse


To be discussed later   :-)   ... watch this blog   :-)

Post Script

There are other equations for the penis and heart.

An equation for the penis in polar form:
    y = Cos(x) + Cos(2x)  polar

Another equation of the heart:
    (y^2 + x^2 - 1)^3 - (x^2)*(y^3) = 0

Here is another one:
    x^2 + (y - (2(x^2+|x|-6)) / (3(x^2+|x|+2)))^2 = 36

Using 2 equations:
    y = (1-(|x|-1)^2)^0.5  and  y = -3(1-(|x|/2)^0.5)^0.5  from -2 to 2

In polar form:
    y = x  polar  (x from -1.5pi to 1.5pi)

Another one in polar form:
    y = (sin(x) sqrt(|cos(x)|) / (sin(x) + 1.4)) - 2sin(x) + 2  polar

And another one in polar form - this equation has a name, called a Cardioid:
    y = 1 - sin(x)  polar
Its corresponding Cartesian equation is:
    (x^2 + y^2 + y)^2 = x^2 + y^2


In 3D

(x^2 + 2.25y^2 + z^2 - 1)^3 - (x^2)(z^3) - 0.1125(y^2)(z^3) = 0
(called Taubin heart surface)


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  1. Amazing!! Completely fall in love with that!! <3 I left my own heart as well..;)

  2. what about the 'poo' curve?

  3. "Of course, you can't talk about love without mentioning the penis."

    I don't think so.

  4. What about the equation for a 3d penis

    1. I'll leave it as an exercise for you :-)

    2. Just parameterize and rotate the peen about the y axis.

  5. Put a=1, b=-0.5 c=1 d=4 you will get testicals

  6. what is a penis? someone please tell me

  7. My penis didnt work, now my friends are laughing at me

  8. Yo, mister! Could you please update the post to include a 3d penis? Thank you in advance!


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