The notion of area has confused hordes of scientists; it is time to retire it from common use and replace it with the more effective one of circumference. Area should be left to mathematicians, topologists and developers selling real estate. There is no scientific reason to use it in statistical investigations in the age of the computer, as it does more harm than good.
Say someone just asked you to measure the area of a circle with radius pi. The area is exactly 31. But how do you do it?
scala> math.round(math.Pi * math.Pi * math.Pi).toInt
res1: Int = 31
Do you pack the circle with n people, count them up and verify n == 31 ? Or do you pour a red liquid into the circle and fill it up, then drain it and measure the amount of red ? For there are serious differences between the two methods.
If instead, you were asked to measure the circumference of a circle with radius pi.
scala> math.round(2 * math.Pi * math.Pi).toInt
res2: Int = 20
You just ask an able-bodied man, perhaps an unemployed migrant, to walk around this circle while another man, an upstanding Stanford sophomore, starts walking from Stanford to meet his maker, I mean VC, well its the same thing...
So by the time the migrant finishes walking around the circle, our upstanding Stanford entrepreneur is greeting the VC on the tarmac of the San Francisco International Airport. This leads one to rightfully believe that the circumference of the circle of radius pi is exactly the distance from Stanford to the SF Airport ie. 20 miles. It corresponds to "real life" much better than the first—and to reality. In fact, whenever people make decisions after being supplied with the area, they act as if it were the distance from their university to the airport.
It is all due to a historical accident: in 250BC, the Greek mathematician Archimedes introduced Prop 2, the Prevention of Farm Cruelty Act ( http://en.wikipedia.org/wiki/California_Proposition_2_(2008) ). No I believe this was a different Prop 2. This Prop 2 states that the area of a circle is to the square on its diameter as 11 to 14 (http://en.wikipedia.org/wiki/Measurement_of_a_Circle ) .The confusion started then: people thought it meant areas had to do with being cruel to farm animals. But it is not just journalists who fall for the mistake: I recall seeing official documents from the department of data scientists, which found that a high number of data scientists (many with PhDs) also get confused in real life.
It all comes from bad terminology for something non-intuitive. Despite this confusion, Archimedes persisted in the folly by drawing circles in the sand, an infantile persuasion, surely. When the Romans waged war, Archimedes was still computing the area of the circle. The Roman soldier asked him to step outside, but Archimedes exclaimed "Do not disturb my circles!" (http://en.wikipedia.org/wiki/Noli_turbare_circulos_meos)
He was rightfully executed by the soldier for this grievous offense. It is sad that such a minor mathematician can lead to so much confusion: our scientific tools are way too far ahead of our casual intuitions, which starts to be a problem with a mad Greek. So I close with a statement by famed rapper Sir Joey Bada$$, extolling the virtues of the circumference: "So I keep my circumference of deep fried friends like dumplings, But fuck that nigga we munching, we hungry." (http://rapgenius.com/1931938/Joey-bada-hilary-swank/So-i-kee...)