Surface area is the total area of the faces and curved surface of the a solid figure. Mathematical description of the surface area is considerably more involved than the definition of arc length or polyhedra (objects with flat polygonal faces) the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces. This definition of the surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration.
General definition of surface area was sought by Henri Lebesgue and Hermann Minkowski at the turn of the twentieth century. Their work led to the development of geometric measure theory which studies various notions of surface area for irregular objects of any dimension. An important example is the Minkowski content of a surface.
While areas of many simple surfaces have been known since antiquity, a rigorous mathematical definition of the area requires a lot of care. Surface area is an assignment
Do you read me, mayday
Aeronaut to base
I confess I'm a mess
No egress
Alone, hovering in space
Is there anyone out there
Why the third degree?
Never knew
Until you
How silence could be so sonorous and deep
Wherever you are
Send out a flare
This is an attempt to connect,
Edify and dissect
Send a light
Send repair
From surface to air
Do you hear me, mayday?
I am in search of
But I'm caught in a knot
Goes to say
So below is as above
Is there anyone out there?
I am high and dry
Suffering is a theme
But reckoning is the only reason why
We suffer at all
To send out a flare
This is an attempt to connect
Edify and dissect
Send a light
Send repair
From surface to air
Is there anyone out there?
Suffering is a theme
But reckoning is the only reason why
We suffer at all
Surface, surface, surface,
It's beginning to show.
To air, to air, to air,
To where you can go.
Abrasion can wear you away.
All you wanted was to go out and play.
Time to fix this crack in the eagle
Before she flies away.
Smokin', smokin', smokin',
Makin' cloudier skies.
Today, today, see the stars.
Two terrestrial minds stay shy.
Monkey, monkey, wanna play around,
But get confused when flames burn your hand.
Got to fix this ache in the eagle
So she can understand.
Surface, surface, surface,
It's beginning to rise.
To air, to air, to air,
To where you can realize your dreams
Brains and beauty can scare you away.
Who knows how much is too much to say?
Try to fix this ache in the eagle
i am me i am real free to take part, in the game
but i don't qualify i never helped to write the rules
and if you see me acting strange please don't hurt me with your scorn
i will not comply it's been the same since i was born
the wisdom of the mystics is the devil's own disguise
his fingers flick the tarot deck keep weak ones mesmerized
what twisted minds would hide behind the cult of living death
man and nature so defiled white dove with hawkish head
what a true man feels defines the world's disease
after centuries his blindness can't be healed
the disappearing sands of time are leaving us no trace
what deity would best describe the mighty human race
has vanity dressed up our god in likenesses of man?
when selfishness and greed and lust are all we understand
what a true man feels defines the world's disease
after centuries his blindness can't be healed
i can't philosophize with you when you don't see the things i do
you don't think beyond the fringe of this tiny world you're in
see me dancing on clouds hear me thinking out loud
true believers, jesus freakers, heaven in your hand
self relying, sanctifying, help me understand
eye of the needle, free the people in the desert land
Please help to make the world you're livin' in better
Please help to make the world you're livin' in better
Please help to make the world you're livin' in better
Please help to make the world you're livin' in better
Please help to make the world you're livin' in better
please help to make the world you're livin' in better
please help to make the world you're livin' in better
please help to make the world you're livin' in better
please help to make the world you're livin' in better
instrumental
Breathing the surface air
I feel that everyone’s alone
And I can hold on tightly
Through all this pain
You seem to go away
It’s only me and you today
I feel
All the rest of this gone away
Gone away
So let me run
Where the sun
Is gone
I’m feel alone
It’s taking me so long to know
Where the sun is gone
I’m feel alone
It’s taking me so long to know
Seeing you walk away
It’s hurting me to play this game
I felt so lost and lonely
So much I wanted
You to say to me
It’s only me and you today
I feel
All the rest of this gone away
The things we used to be
So let me run
Where the sun
Is gone
I’m feel alone
It’s taking me so long to know
Where the sun is gone
I’m feel alone
It’s taking me so long to know
So let me run
Where the sun
Is gone
I’m feel alone
It’s taking me so long to know
Where the sun is gone
I’m feel alone