The area of a disk (the region inside a circle), often incorrectly called the area of a circle, is πr2 when the circle has radius r. Here the symbol π (Greek letter pi) denotes, as usual, the constant ratio of the circumference of a circle to its diameter. It is easy to deduce the area of a disk from basic principles: the area of a regular polygon is half its apothem times its perimeter, and a regular polygon becomes a circle as the number of sides increases, so the area of a disk is half its radius times its circumference (i.e. 1⁄2r × 2πr).
Modern mathematics can obtain the area using the methods of integral calculus or its more sophisticated offspring, real analysis. However, in Ancient Greece the great mathematician Archimedes used the tools of Euclidean geometry to show that the area inside a circle is equal to that of a right triangle whose base has the length of the circle's circumference and whose height equals the circle's radius in his book Measurement of a Circle. The circumference is 2πr, and the area of a triangle is half the base times the height, yielding the area πr2 for the disk. Prior to Archimedes, Hippocrates of Chios was the first to show that the area of a disk is proportional to the square of its diameter, as part of his quadrature of the lune of Hippocrates, but did not identify the constant of proportionality.
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It walks in circles all the time
Different mind
It claws the walls with bound hands
and tries to climb this shell that grew inside
It keeps correcting all its non-existant
flaws while it pretends they're gone
It knows the mind that's keeping track
of all mistakes that ever made its life
Sometimes I can almost reach the sun
Yet, the distance
Is blinding
It walks in circles all the time
Different mind
It keeps repeating all its goals to make
the purpose seem so worthwhile
It inputs air into the lungs just so they
see that it pretends to breathe
It ran the circle one last time
One last time
Abandoned all these faces
living in the dreams
that emptied out its cries
It climbed the wall on broken hands
until the edges pulled apart
Revealing all the same divides
We are alive, to see the end of us
Struggling to reach the finish line
To designate our time to questionable lives
So called meaningless, still there's no answer
For this vulnerable reality comes
Can't we break the cycle in which we reside ?
Trigger the silence and make up your mind
See what's inside
Into shimmering sleep, I risk it all
It takes the soul out of me, can't change for good
Falling back into patterns, my destiny
Ambitions in me put to shame
The faceless have come, serving the cycle
Feeding the urge for security
Oppression suppressed
Expression is a form of art condemned
We need to control our second nature
Creating artificial projections of life
In which our instincts will succumb
We're building a new world
And you kneel down to welcome the meaningless
Silence is timeless
And finally we're breaking out
Objective achieved, the perfect machine
We're drawing circles every day
It takes only one step to be on your way
Reflection, our time's up
And over and over again
Again, again
Trying to break out, escape
Feel the rush, just like everyone
Look back within
Then I feel a little closer
To the thief inside of me
I censor my flaws
But it's only a matter of time
Before the walls tumble down
Did I get any closer?
Wake up, take it all
Only to lose the things I love
When I fall
Poison, she will willingly
Collide, in through beneath her
Use and situate me, blending
All the colors here, all around me
As I wipe this stain up from my hands
I realize it's all I have that's sacred from you now
Here is where your honesty lies
And it's digging in to feed here
Soul succumbing to be the beginning
Of this empty shell here cracked and bleeding
A painful truth becomes a searing needlepoint
Beyond the pain, behind a wall, into the womb
You circumcise a painful point to cut around
Circular pizza coming my way and I'm not afraid to let it
shine
Wait for the day when I love you again and I own my right
cos I'm on time
Don't you understand that this feeling can't last long
If you don't take her hand and be sure keep holding on
(x2)
1 2 3 4
I wish I was a fairy queen running through the grass
I'd climb up all the rocks and trees and slide down on my
siempre es terminar para volver a empezar
el punto de partida es el de llegada
y vuelvo a recorrer el circulo sin fin
que nunca voy a terminar x2
el tiempo es un rincón donde no se deja ver
en este viaje sin pasado ni futuro
y si lo que vendrá no sera lo que fue
ya nunca lo voy a saber x2
voy dando vueltas voy por ahí
me da lo mismo frenar que seguir
y aunque no dejo de caminar no voy a ningún lugar
la lluvia del mar la sombra de dos
las marcas del sol... un ruiseñor el viento del sur memoria fugaz la orilla de luz
estrella de sal
siempre es terminar para volver a empezar
el punto de partida es el de llegada
y vuelvo a recorrer el circulo sin fin
que nunca voy a terminar x2
voy dando vueltas voy por ahí
me da lo mismo frenar que seguir
y aunque no dejo de caminar no voy a ningún lugar
la lluvia del mar la sombra de dos
las marcas del sol... un ruiseñor el viento del sur memoria fugaz la orilla de luz