self portrait

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A cat's self portrait as a tiger  :-)

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Where is mom?

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To mom:
    I'm hungry ...
    I'm cold ...
    I'm hot ...
    Can I have ... ?
    I want to watch ...
    Where are you ?
    Can you ask Dad ?
    Can you help me ... ?
    He hurt me ...
    She hurt me ...
    I want to go there ...
    When are we ... ?
    Why are we ... ?
    Why can't we ... ?

To dad:
    Where is mom ?

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Mother drinks because of you

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Don't forget to pick up a bottle of wine for your mom on Mother's Day.
After all, you are one of the reasons she drinks.

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Pont Neuf Bridge, Toulouse, France

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Dear friends and colleagues,

Over the past few weeks,
I have received many funny images or jokes and
I have emailed them to friends and colleagues
who I thought shared the same sense of humour.

Unfortunately, I seem to have upset a few people
and received criticism for being
sexist and shallow.

So, from now on,
I am only emailing content of general interest
to all persons of sensibility and good taste.

Content such as:
    - natural beauty
    - phenomena
    - places of historical significance
    - or general interest.

I am sure you will all agree the attached picture
of the Pont Neuf Bridge, Toulouse, France,
has great historical value
surrounded by phenomenal natural beauty.

Thanks and regards

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Eye sight failing

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Don't stress about your eyesight failing as you get older.
It's natures way of protecting you from shock as you walk pass the mirror.

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Fat - When you realize it, it is too late

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The past of eat is ate.
And the future of ate is weight.
And the most funny part is that people realize it when it is late.

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Iridescent cloud

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An iridescent cloud ~~~

It is an uncommon phenomenon, the result of diffraction ... small droplets of water or small crystals of ice individually scattering light.

If the small droplets/crystals are of similar size, their cumulative effect is seen as iridescent colours. The cloud must be optically thin, so that most rays encounter only a single droplet. Iridescence is therefore mostly seen at cloud edges or in semi-transparent clouds.

You may have seen this type of cloud in your own travel, or seen more colourful photos on the internet.  But it is so much sweeter if you can capture it with your own camera.

Above photo was taken on 2015 March, during a climbing trip to Gungartan Mountain in Kosciuszko National Park in NSW, Australia. Photos and trip report of that climb are in:
http://mntviews.blogspot.com.au/2015/03/gungartan-kerries-ridge-nsw-australia.html

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Acripeza reticulata (Mountain Katydid)

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Acripeza reticulata (Mountain Katydid, also known as Mountain Grasshopper) ~~~
The one on left and also the one on top-right is a female. When its wings are folded, it looks like a small lump of dirt and is not easy to be spotted. But when its wings are spread out, you can see the beautiful red, blue & black bands on its body.
The male is much skinnier - bottom-right.

Just looking at the photo, you wouldn't have imagined they are the same insect !

Above photo was taken in 2015 March, during a climbing trip to Gungartan Mountain in Kosciuszko National Park in NSW, Australia. Photos and trip report of that climb are in:
http://mntviews.blogspot.com.au/2015/03/gungartan-kerries-ridge-nsw-australia.html

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Money & Grave

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Man chases money into grave.

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Women are always right !

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Men to the left because women are always right !

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Cleavage is like the sun

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Cleavage is like the sun.

You can glance at it for only a second,
but if you wear sunglasses,
you can look much longer.

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Spelling error

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I hate spelling errors.

You mix up two letters
and your whole post is urined.

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Penis guard

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Penis guard for man on beach

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Smiling face in the night sky

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Say Cheese !

In the centre of the below image, taken with the NASA/ESA Hubble Space Telescope, is the galaxy cluster SDSS J1038+4849 ... and it seems to be smiling.

You can make out its two orange eyes and white button nose. In the case of this “happy face”, the two eyes are very bright galaxies and the misleading smile lines are actually arcs caused by an effect known as strong gravitational lensing.

Galaxy clusters are the most massive structures in the Universe and exert such a powerful gravitational pull that they warp the spacetime around them and act as cosmic lenses which can magnify, distort and bend the light behind them. This phenomenon, crucial to many of Hubble’s discoveries, can be explained by Einstein’s theory of general relativity.

In this special case of gravitational lensing, a ring (known as an Einstein Ring) is produced from this bending of light, a consequence of the exact and symmetrical alignment of the source, lens and observer and resulting in the ring-like structure we see here.

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Fart to smell like mint :-)

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This is fartbulously fartastic ... An underwear patch to make your farts smell like mint  :-)
And when will Apple buy it and name it iFart?

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Clock

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A smart ass recursive clock  :-)

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Politician and Prostitute

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Hi! I'm 32. I'm a politician and I'm honest.
Hi. I'm 29. I'm a prostitute and I'm a virgin.

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Wolf Spider

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The wolf spider is the only species of spider that carries its offspring this way - live, hatched and wriggling on her back!
After a gestation of 9 to 27 days (dependent on temperature) during which the eggs are carried around in a silk globe attached to the mothers stomach, the offspring hatch and climb on to her back. They stay there until they're ready to hunt alone.

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What is wrong with this picture?

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Something is not right with this picture.
Can you see it?

(Answer is in the comment section.)

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Jelly Fish has no brain

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The fact that jellyfish have survived for 650 million years despite not having a brain is great news for stupid people.
(Actually, this is great news for the human race too, and especially me. But wait, that means people in my office will be there forever.)

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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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Photography trick or car

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How to take a photo of vintage cars on the road.

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Women are like cars

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Women are like cars. You can trade her in for a newer & younger model. But when you miss your old car, it'll have become a classic and out of your price range.

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How can this happen ???

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Truck jackknifed between tree and another truck

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Jewellery used as a remote control

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The first remote control device ever invented ...
to open a girl's legs.

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Stars

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Which do you prefer; 5-star or 5 billion stars ?
Answer: The one with a movie star in it.

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Karma is like dominoes

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Karma - it is like this man pushes dominoes ... they will eventually fall over him.

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Halloween nowadays

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Do you have gluten-free treats, lady ?
I'm lactose intolerant.
I can't eat nuts.
I am caramel-phobic !
Do you have vegan chocolate ?
I have a nougat allergy.
Gender neutral candy ?
Organic Only !

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Astrology

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The stars and planets will not affect your life in any way.

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Universe is made up of Morons

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Scientists say the universe is made up of protons, neutrons and electrons. They forgot to mention morons.

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Find cat

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For all you cat lovers, can you find the one cat amongst 99 dogs?

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Why doesn't Osmosis work ?

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Why doesn't osmosis work in study - from high info to low info?

Because gravity sucks !

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Plastic packaging

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One shark to another: "There's so much plastic packaging on food these days."

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Spaceship lifts off on moon

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Astronaut mumbling to himself

Man, in this low gravity
I feel like I can lift anything !
I bet I could even lift up the ship !

Hya !

... Oh crap !

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Both are grey colour!

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Both blocks are grey in colour. Use your finger (or a strip of something) to cover the middle section and observe !

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In a pub - dog painted on the stomach of a man

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In a pub ... "No, I do not wish to see his tail wag."

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Optical illusion - moving oranges

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If you move the computer screen rapidly up and down, or use the scroll bar to move the browser window rapidly up and down, you can see the central square moving !

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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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