Mathematical equations for breasts

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Simple curve

A simple mathematical equation
for a buxom lady's breasts:

y = (1 - (|x|-1)^2)^0.5
   which is equivalent to
y = Sqrt(2*|x| - x^2)

A plot of the real part of the breasts,
ignoring the imaginary part  :-)

Not good enough for you ?
Try the next one !



More realistic curve

y = Sqrt(1 - (|x|-1)^2) + Sqrt(0.01 - (x+1)^2) + Sqrt(0.01 - (x-1)^2)
   which is equivalent to
y = Sqrt(2*|x| - x^2) + Sqrt(0.01 - (x+1)^2) + Sqrt(0.01 - (x-1)^2)

A plot of the real part of the breasts,
again ignoring the imaginary part  :-)

More complicated equation

This one was taken from somewhere
on the internet few years ago.
Unfortunately, now I couldn't find the source
nor the author anymore  :-(

y =
   sqrt(1 - (x+3/2)^2 / (1+(x+3/2)^10)^(1/5))
+ sqrt(1 - (10x+15)^2 / (1+(10x+15)^10)^(1/5)) /10
+ sqrt(1 - (x-3/2)^2 / (1+(x-3/2)^10)^(1/5))
+ sqrt(1 - (10x-15)^2 / (1+(10x-15)^10)^(1/5)) /10

3D surface

A 3D surface for breasts:

z = 4*x*y - x^4 - y^4

Source:
https://www.chegg.com/homework-help/questions-and-answers/surface-z-4xy-x-4-y-4-graphed-two-absolute-maximums-find-values-maximums-q11144119



Other mathematical equations for:
Heart, Bum, Penis, Boomerang

They are covered in my blogs:
https://onemanadreaming.blogspot.com/2014/08/mathematical-equation-of-love-heart.html
   and
https://onemanadreaming.blogspot.com/2014/04/from-golden-ratio-to-golden-arse.html

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Understand limit

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Mathematics - understanding a limit  :-)

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Calculated risk

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The risk I took was calculated.
But man, am I bad at math !

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Inifinity

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Nine: "I'm greater than you!"
Eight (lying down): "What about now?"

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Math for grownups

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Math for Grownups:

Cheeseburger + Detox tea
       = Total health

30 minutes productivity + 6 hours internet
       = Good work day

1 hour gym time + 4 hours couch time
       = Total fitness

1 sale item + 10 impulse purchases
       = Good budgeting

2 hours sleep + 4 cups of coffee
       = Awake & alert

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Mathematical equations of love, heart, penis and the boomerang

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Love

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.


Heart

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

To see the above graph,
go to WolframAlpha website
        http://www.wolframalpha.com/
        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:
http://math.stackexchange.com/questions/902120/is-there-a-name-to-this-equation-y-axb2-cx2-d

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 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.


Boomerang

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

Penis

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

The mathematical equation of an aroused penis is:
    y = |sin(x)| + 5*exp(-x^100)*cos(x)  from -3 to 3

Type the above into Wolframalpha to produce

A limp penis:
(by ShmemicalShmengineer in Reddit)
    0 = 2.8x^2(x^2(2.5x^2+y^2-2)
                     + 1.2y^2(y(3y-0.75)-6.0311)+3.09)
          + 0.98y^2((y^2-3.01)y^2+3) - 1.005

A fat one in polar form:
    y = Cos(x) + Cos(2x)  polar

The Bum

This is covered in my blog
From Golden Ratio to golden arse
http://onemanadreaming.blogspot.com.au/2014/04/from-golden-ratio-to-golden-arse.html


Breast

This is covered in my blog
Mathematical equations for breasts
https://onemanadreaming.blogspot.com/2022/04/mathematical-equations-for-breasts.html

Here is one equation from the above link
for a pair of breasts:

y =   sqrt(1 - (x+3/2)^2 / (1+(x+3/2)^10)^(1/5))
     + sqrt(1 - (10x+15)^2 / (1+(10x+15)^10)^(1/5)) / 10
     + sqrt(1 - (x-3/2)^2 / (1+(x-3/2)^10)^(1/5))
     + sqrt(1 - (10x-15)^2 / (1+(10x-15)^10)^(1/5)) / 10

Above equation was taken from somewhere
on the internet few years ago.
Unfortunately, now I couldn't find the source
nor the author anymore  :-(


Post Script

There are other equations for 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

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

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From Golden Ratio to golden arse

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In mathematics,
two quantities are in the golden ratio φ
(phi, or 1.6180339887...)
if their ratio is the same as the ratio of their sum
to the larger of the two quantities.

Geometrically, the golden ratio represented as
a line divided into two segments, "a" and "b",
such that the entire line
is to the longer "a" segment
as the "a" segment is to the shorter "b" segment.

Expressed algebraically,
for quantities a and b,
with a > b

Many artists and architects have proportioned
their works to approximate the golden ratio ...

especially in the form of the golden rectangle,
in which the ratio of the longer side
to the shorter side is the golden ratio ...

believing this proportion to be
aesthetically pleasing.

In geometry, a golden spiral is a logarithmic spiral
whose growth factor is the golden ratio φ (phi).

That is, a golden spiral gets wider
(or further from its origin)
by a factor of φ for every quarter turn it makes.

Below is the figure of
an approximate and true Golden Spirals.

The green spiral is made from quarter-circles
tangent to the interior of each square,
while the red spiral is a Golden Spiral.

Overlapping portions appear in yellow.

The length of the side of one square
divided by that of the next smaller square
is the golden ratio φ (phi).

Now, what do you get
when you put 2 golden spirals together ? ...

A most aesthetically pleasing Golden Arse !

All very well, you say.
But what can you do with a Golden Arse ?

Ah, you must check out this link ==>
https://onemanadreaming.blogspot.com.au/2014/04/income-tax-query.html

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Clock for mathematicians

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To all you budding mathematicians ... what is wrong with this clock?

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128Ve980 - I LOVE YOU

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Guy: Can you solve this? (128Ve980)
Girl: Hmmm ... I can't.
Guy: So, I erase the top half.

I LOVE YOU

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Mathematical Puzzle

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a = 0.99999...
10a = 9.99999...
10a = 9 + 0.99999...
10a = 9 + a
9a = 9
a = 1
1 = 0.99999... !!!

Actually, there is no discrepancy.

Although the above proof lacks
mathematical vigour, but ...

In mathematics, the repeating decimal 0.99999...
can be shown to be equal to the number 1.

In other words, the symbols 0.99999... and 1
represent the same number.

Refer Wikipedia:  http://en.wikipedia.org/wiki/0.999

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Proof of Pi = 4 ?

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Draw a circle.
Draw a square around it.  Perimeter = 4
Remove corners.  Perimeter is still 4 !
Remove more corners.  Perimeter is still 4 !
Repeat to infinity.
Pi = 4 !

Problem Archimedes ?

The more general question is:

If you approximate a curve
by a series of straight lines,
how do you know
when you use smaller and smaller straight lines,
in the limit,
the sum of lenghs of these small straight lines
will be the length of the curve ?

I suspect it has something to do with
differentiability.

If you approximate a curve
by smaller and smaller corners,
in the limit,
the 1st order differential of the resulting curve
is no where continuous.

Whereas if you aproximate the curve
by the hypotenuse of the small corners,
the resulting curve's 1st differential
will be continuous when the hypotenuses
become smaller and smaller.

Thus the lenghts of the hypotenuses
will be able to approximate the length of the curve.

I will leave you to fill in the missing details
on why a continuous 1st order defferential
will enable the lengths of a series of
small straight lines to be able to approximate
the length of the curve.

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