Both blocks are grey in colour. Use your finger (or a strip of something) to cover the middle section and observe !
Thursday, August 28, 2014
Saturday, August 23, 2014
Monday, August 18, 2014
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 !
Wednesday, August 13, 2014
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
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
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:
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
This is covered in my blog From Golden Ratio to golden arse
To be discussed later :-) ... watch this blog :-)
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
(x^2 + 2.25y^2 + z^2 - 1)^3 - (x^2)(z^3) - 0.1125(y^2)(z^3) = 0
(called Taubin heart surface)