Additional Math Pages & Resources

Wednesday, October 21, 2009

How can you be SO DENSE!

Density means being "thick" (as in - you didn't do what your brother / sister / parent expected!). But it also means more than that.

Mathematically speaking, density is equal to mass ÷ volume.  It's stated in units like kilos per cubic meter, or grams per cubic centimeter. When talking about populations, it is expressed as people per square mile or kilometer.

Density is a subject that interests me. Remember the blog about the Thunderbolt Darjeeling tea leaves and how tea of the same weight can result in different-sized packages? That's an example of relative density.

Well, in playing with Wolfram Alpha, a web search/calculation engine, I was able to uncover some interesting facts about density - let's see if we can use it to answer a few questions:

Question: What are the relative densities of water and diamonds?

Answer: Diamonds are 3.5 times as heavy as water.

Question: What are the relative densities of water and gold?

Answer: Gold weighs 19.3 times as much as water. Platinum weighs 21.1 times as much as water.

Question: What are the relative densities of air and helium (for those party ballons)?

Answer: Helium is one-fifth the weight of an equivalent amount of air (at the same altitude/pressure).

Now how about population density? If your neighborhood seems crowded, you could move to the Falkland Islands, where the density is one person per square mile. How does that compare with the rest of the world?

Fact: Macau, an island off the Chinese mainland near Hong Kong, has the highest population density in the world. About 44,000 people per square mile. Despite the crowding, the citizens of Macau also have the longest life-expectancy in the world - 84.4 years.

Fact: Greenland is the least-dense population, with only .07 people per square mile. And their life expectancy is 70.1 years.

Fact: Swaziland in Africa has 172 people per square mile, but sadly their life expectancy is only 31.9 years.

Wolfram Alpha can do many other cool things, like building a population density map. What do you think of it?

Moving on...

Question: What is the population density of San Diego county?

Facts:  San Diego County has a population of 3 million, spread over 4200 square miles of land area.

Answer: 3,000,000 ÷ 4200 = 714 people per square mile. And life expectancy of 78 years.

Of course, if you get bored with density, Wolfram Alpha lets you calculate strange things of any sort:

Question: What is the median age of people living today?

Answer: Approximately 27.5 years old. It ranges from 45.5 years in Monaco to 15 years in Uganda.

Fact:  I am older than the median age in ANY country, and more than twice as old as the global median age - but probably still have a few decades to go - I hope!

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