One man's Funnies: Heart

Showing posts with label Heart. Show all posts

Sunday, April 29, 2018

A teacher's heart

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Doctor to teacher:
"Your heart is slightly larger than the average human heart, but that's because you're a teacher."

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Please visit my main page at http://mntviews.blogspot.com/

Sunday, January 8, 2017

You'll have to admire Alexa who has given her big heart to hiking :-)
This photo was taken in May 2016 at Rigby Hill in the Blue Mountains Nat Pk, NSW, Australia.
Photos and trip report on the Rigby Hill climb are in my blog:
http://mntviews.blogspot.com.au/2016/05/rigby-hill-victoria-falls-nsw-blue-mts.html
See photo #52 in the blog.

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Please visit my main page at http://mntviews.blogspot.com/

Thursday, April 14, 2016

Heart-shaped pool

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This heart-shaped pool is at Diamond Head, Crowdy Bay National Park, NSW Central Coast, Australia.
More photographs of the lovely Diamond Head headland are in my blog:
http://mntviews.blogspot.com.au/2015/11/diamond-head-nsw-australia-2015-11.html

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Please visit my main page at http://mntviews.blogspot.com/

Wednesday, August 13, 2014

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