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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https://mntviews.blogspot.com/
The A26 road in Sri Landa ... It starts at Kandy, passes through Digana, Teldeniya, Medamahanuwara, Hunnasgiriya, Udadumbara, Mahiyangana and Belilgalla to reach Padiyathalawa. It is well known for its 18 consecutive hairpin turns.
+between+Kandy+&+Padiyathalawa.jpg)
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Christ the Redeemer of the Andes (Spanish: Cristo Redentor de los Andes) is a monument high in the Andes at 3,832 metres (12,572 ft) above sea level on the border between Argentina and Chile. It was unveiled on 13 March 1904 as a celebration of the peaceful resolution of the border dispute between the two countries.
The statue is located at the pass of La Cumbre, the highest point on the old road between Mendoza in Argentina and Santiago de Chile. The pass is also known as the Church (Iglesia) Pass on the Chilean side and the Bermejo Pass on the Argentine side. The road climbs 1 km over a sinuous 9 km from Las Cuevas (the closest village at the foot of the climb) to the pass.
The road is now principally used as a tourist route to visit the statue, with the main route between the two countries now using the Cristo Redentor Tunnel at the foot of the climb.
Source: http://en.wikipedia.org/wiki/Christ_the_Redeemer_of_the_Andes
Photos are by me ... I was there in 2009 January.
It is well worth a visit.
Aconcagua, the highest mountain in South America, is that big mountain to the right of the centre of the above photo. I climbed it a few days earlier ... write up and photos of the Aconcagua climb are in my blog:
http://mntviews.blogspot.com/2009/01/2009-jan-argentina-aconcagua.html
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For all you budding outdoor enthusiasts ... here is how to identify that light in the sky.
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Goblin Shark (Mitsukurina owstoni) is a rare, poorly understood species of deep-sea shark. Sometimes called a "living fossil". This pink-skinned animal has a distinctive profile with an elongated, flattened snout, and highly protrusible jaws containing prominent nail-like teeth. It is usually between 3 and 4 m (10 and 13 ft) long when mature. Goblin Sharks inhabit upper continental slopes, submarine canyons, and seamounts throughout the world at depths greater than 100 m (330 ft), with adults found deeper than juveniles.
The long snout is covered with ampullae of Lorenzini that enable it to sense minute electric fields produced by nearby prey, which it can snatch up by rapidly extending its jaws.
Source: http://en.wikipedia.org/wiki/Goblin_shark
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Two dramatically contrasting chess puzzles:
The first one is gauchely complicated. Its solution is fiendishly difficult to find - completely from the left field. You just have to marvel at the devilish mind of the composer.
By contrast, the 2nd one is elegantly simple. Although the solution is easy to find; and yet you are left marveling at the ingenuity of the composer who made the White pieces dance so gracefully over the board.
Puzzle 1 - White to move and mate in 3. Solution is in the comment section.
Puzzle 2 - White to move and win. Solution is in the comment section.
All my posts on chess can be found by clicking ==>
http://onemanadreaming.blogspot.com/search/label/Chess%20puzzle
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This morning ...
I was beaten up by a busty woman in an elevator.
I was staring at her boobs when she said,
"Would you please press one?"
So I did.
I don't remember much after that.
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Coconut crab:
Largest land-living crab in the world
with a weight of up to 4 kg (9 lb)
It can grow to up to 1 meter (3 feet) in length
from leg to leg.
It is found on islands across the Indian Ocean
and parts of the Pacific Ocean
as far east as the Gambier Islands,
mirroring the distribution of the coconut palm.
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https://mntviews.blogspot.com/
A recent study has found women who carry a little extra weight live longer that the men who mention it.
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Happy Mother's Day to the person who usually gets stuck with feeding me, and walking me, and cleaning up after me, and taking me to the vet's, and hugging me, and worrying about me.
-- From the dog
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I'm not saying I am Wonder Woman. I'm just saying no one has ever seen me and Wonder Woman in the same room.
Kid 1: "See, I told Ya!"
Kid 2: "So, that's how she does it."
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Claustrophobia is the fear of closed spaces. For example, I'm on my way to a liquor store right now and I'm afraid it might be closed.
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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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https://mntviews.blogspot.com/
The secret of enjoying a good wine.
1. Open the bottle to allow it to breathe.
2. If it does not look like it is breathing, give it mouth to mouth.
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"Hello, is this Miss Singleton ?"
"Yes, it is."
"Miss Singleton,
This is John Smith, your tax accountant.
I must inform you,
your tax statement was rejected.
They say that your salary and your possessions
are incompatible ...
... Your salary as a secretary is too low
for you to be able to afford:
- a luxury apartment
- a new Mercedes-Benz
- expensive clothing
- jewelry
- vacations in Europe
- etc."
"Oh, and what can I do about it Mr Smith ?"
"Well, let's do the following:
Send me a recent copy of
your principal source of income,
and I'll see what I can do with it."
"Very well Mr Smith.
I am making a photocopy of it now,
and I will email it to you shortly."
Well, she must have the Golden Arse ...
Check out this link for an explanation ==>
https://onemanadreaming.blogspot.com.au/2014/04/from-golden-ratio-to-golden-arse.html
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https://mntviews.blogspot.com/
An entire hill slid over National Highway No 3,
close to Keelung in north Taiwan.
The landslide happened on 2010-04-25
and I was on this highway few days earlier.
Jesus ... that was too close for comfort.
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