Can you solve this 6th grade math problem?

[pocaracas]

Math is fun

Math isn't fun, math is bad spelling. Maths, on the other hand, is fun.

Really?

http://www.dictionary.com/browse/math?s=t
""
noun
1. mathematics.

Origin of math
shortened form
""

Same goes for Maths... curious...

[Whateverist]

I think the colour (sic) of your spelling is as strange as your pronunciation of aluminum.  (Notice there is only one "i" at the end of that word and it is too busy providing the "min" we agree on to also offer the "i-um" you give it.)

Hey, I'm Irish. While I know the Queen's english I don't use it. The way I pronounce aluminium is "bendy metal".

I apologize for slandering you so viciously.  I never meant to imply your were an Englishman.  Please forgive me.

[pocaracas]

Math isn't fun, math is bad spelling. 

I think the colour (sic) of your spelling is as strange as your pronunciation of aluminum.  (Notice there is only one "i" at the end of that word and it is too busy providing the "min" we agree on to also offer the "i-um" you give it.)

The other day, I heard a story about the aluminum/aluminium split.
The way it went was:
Way back when the stuff was "discovered", the British guy that did it named it "Aluminum". This word traveled to the US and there took hold.
In comes a guy (possibly the same one) who looked at the other metals and noticed that they had a certain ending... the -ium, as in chromium, Callium, Germanium, Indium, Vanadium, Titanium, Lithium, Magnesium, Potassium, Calcium, etc...
So he decided to make Aluminum end in -ium.... and came up with Aluminium.
That came to be the official English spelling of the element.
But the US had already been contaminated by Aluminum and cared not for "official English"...

[Thumpalumpacus]

I really don't think someone needs to be a 'math whiz' to follow my explanation.  And since when is English not 'the language of science'?  

Boru

You're trying to pick a fight. Not interested.

lolz

[LastPoet]

So, what I said, only I said it in English.

... and you didn't show your work, making your answer that much less useful.

Watch out Thump. Soon we will be involved in a semantic discussion, that will evolve into passive aggressiveness that everyone is against him.

This one never changed, just changed tactics. The fucker has a valve that doesn't allow him to accept to be wrong, everyone else is. Oh I better shut up, else he will start crying about how mean we are to him.

[Faith No More]

I couldn't remember the formula for the area of a circle.  I haz a sad.

I remember a math teacher of mine once saying something to help us remember like "pie are squared, not round."

[Thumpalumpacus]

... and you didn't show your work, making your answer that much less useful.

Watch out Thump. Soon we will be involved in a semantic discussion, that will evolve into passive aggressiveness that everyone is against him.

This one never changed, just changed tactics. The fucker has a valve that doesn't allow him to accept to be wrong, everyone else is. Oh I better shut up, else he will start crying about how mean we are to him.

I know, that's why I simply edited my post to just laughter. If a person cannot see their own part in a problem, it's not my job to point it out, especially if the only thanks will be endless justification attended with insult.

[Jackalope]

Just saw this on youtube... after the first 10 seconds, I got it... then noticed that the video was 9 minutes long! O.o

All you brainiacs take it easy and let's see how others do it!

THE PROBLEM:

Find the total area of the red spots.




That's a normal rectangle, with two equal circles inside.
Looks odd, at first, but it's remarkably simple.

---

21.46

(20 * 10 - (2 * pi * 5^2))/2.

---

[Whateverist]

I think the colour (sic) of your spelling is as strange as your pronunciation of aluminum.  (Notice there is only one "i" at the end of that word and it is too busy providing the "min" we agree on to also offer the "i-um" you give it.)

The other day, I heard a story about the aluminum/aluminium split.
The way it went was:
Way back when the stuff was "discovered", the British guy that did it named it "Aluminum". This word traveled to the US and there took hold.
In comes a guy (possibly the same one) who looked at the other metals and noticed that they had a certain ending... the -ium, as in chromium, Callium, Germanium, Indium, Vanadium, Titanium, Lithium, Magnesium, Potassium, Calcium, etc...
So he decided to make Aluminum end in -ium.... and came up with Aluminium.
That came to be the official English spelling of the element.
But the US had already been contaminated by Aluminum and cared not for "official English"...

Well then by the rule of "black, black, no takes back" the spelling must remain as we 'muricans spell and say it.

[Alex K]

What quantum divergences are you referring to? 

Are you (a) being serious with this, or (b) is it only a joke?

My bolding.

The quantum answer is b.

The answer is a quantum superposition of (a) and (b): It's a silly joke with a relatively deep background in mathematics and physics.

My bolding.

The answer is b.

That's too bad if that is the case. He gave a particularly intriguing answer, I was looking forward to him explaining it.

It is a joke, but it has enough real content that you shan't be disappointed:

In quantum field theory, many quantities such as the masses of particles and the strength of particle interactions at first come out as infinite, and upon closer inspection one realizes that this "infinity" appear because one has missed a crucial feature: these quantities are not fixed numbers, but depend on the scale at which one is examining the physical system.

For example, the strength of the so-called "strong force" gets weaker, the higher the energy of the collision is. A very good understandable analogy is given by fractals such as the length of a shoreline. The more fine-grained the scale is at which you measure the length of a shore line, the longer it becomes, and if you describe the shoreline by a mathematical fractal, the length actually goes to infinity if you measure it down to infinitely small scales. The properties of particles in quantum theory, it turns out, behave very similarly.

So my joke (I love explaining jokes) consisted of taking something as pedestrian as the geometric shapes in the OP and acting as if we were dealing with subtle quantum phenomena. However, this joke might not be all that far from the truth if you really look at it: If you think of the shapes in the OP as something actually drawn on a piece of paper, there are two effects which go in the direction of my facetious comment.

Once you examine an actual drawing down to small scales, the coarse molecular nature of the paper and the ink will become apparent and the true definition of what the area is becomes fuzzy. On a more fundamental level, if you think of the shapes in the OP as something that is actually sitting in physical space (as opposed to being a mathematical abstraction), once one examines the quantum nature of space itself, the same weird scale-dependence of measured values (such as areas) will likely show up again, just like they appear with particles in quantum theory, or with the length of fractal shorelines. The problem is namely that once you try to examine the area of the drawing down to the Planck scale, the quantum fluctuations of space itself can let the area appear infinitely large if you look close enough, because the surface of the drawing might become fuzzy, a bit like a fractal, due to the quantum uncertainty in the geometry of space itself.