Additional Math Pages & Resources

Tuesday, May 31, 2011

Creative Units of Measure, Part I

This week I am traveling. I thought I'd better find something interesting for the blog, but not too difficult for me to organize while I am out of the office. It seemed fitting to spend a few days on how we create new measurement units to clearly describe new situations.

(Remember, this blog is about how grown-up people use elementary math skills in real life.)

Today I read about billionaires who, despite the current economy, are still buying enormous yachts. About 2000 people own most of the 4000+ yachts in the world that are over 100 feet (30 meters) long.

We've done blogs on large ships before, in Capsize or Capesize, but they were not privately-owned luxury vessels.

The article I read today cited a decline in the number of ships delivered, due to the weak economy. However, while the number of ships declined, the aggregate yacht length (all of them placed in a line bow-to-stern) of luxury vessels on order has increased.

This creative unit of measure accurately reflects the fact that PEOPLE WHO ARE STILL BUYING are SPENDING MORE. Their ships are getting larger.

I suppose this is like saying the number of wedding rings sold this year declined, but the number of carats of diamonds on those rings increased.

I tried a few different approaches, but I can't line up 8,008 meters of yacht across the page on the blog. So we'll just have to look at some of the motor yachts in a vertical line-up. Below you will see the three largest sailing yachts in the world.

By the way, you can charter the Maltese Falcon sailing yacht (the last one) for around $500,000 a week and take 11 of your best friends along. That's $41,666 per person, or about $6000 a day. Per person.

Friday, May 27, 2011

Math weather you like it or not

This week we've been looking at the use of simple fractions and percentages when describing the weather and climate.

Weather is the atmosphere's behavior right now - the temperature, humidity, visibility, wind, brightness, cloudiness, precipitation and atmospheric pressure changes.

Climate means a long-term (30 years) average pattern of weather in a particular area, including temperature, humidity, sunshine, wind, precipitation, fog, frost, storms, etc.

I was amused by this description, which I found on the NASA website - Climate is what you expect, but Weather is what you get. Like it or not.

Math is a tool we use to measure the weather and calculate the climate.

I searched for weather and math on Google Web. I got 46 million hits in .15 seconds. I read ten of those and got depressed.

I searched again in Google News. This time I had 484 results. The first hit was professor Cliff Mass in Seattle, talking about weather and math and the need for better math education. Read it if you wish.

My third search was weather and math on Google Images. This provided 11.6 million hits in .33 seconds. Here's the first image that came up, from Mr. Taylor's Science Website (now "inactive"). It shows the water cycle through the earth and atmosphere. [click image for a larger view]

Moving along, a Video search turned up 1830 videos in .15 seconds. That doesn't mean there are 1830 videos on mathematicians doing weather predictions - one of the links led to Weather After Math (a nice thought) but the author meant to say Weather Aftermath (an entirely different thing).

A search for weather math in Shopping located 7,340 products that I could buy, ranging from $1 to $350 (I discarded 2 outliers).

Did you know you can search the full text of books on Google? I found 95,400 occurrences of weather and math in books that Google has indexed, including the NY Times bestseller Kiss My Math by Danica McKellar.

Moving along to YouTube, I located 934 videos on weather and math.

I went to Patent Search and dug up 335 patent citations. One patent described a grid of satellites to control the weather. The claimant says his invention can generate energy, reclaim wasteland, and improve the environment. Satellites with big sun vanes would orbit the planet, reflecting the sun's rays back out into space and/or generating solar energy. The combination of this shade and "free" energy would enable us to selectively adjust global weather. However, the last page of the paper says:

Should we do the math on the price and risk of implementing this invention? Whether he means one million or one billion satellites, I'm not expecting implementation in my lifetime ...

Thursday, May 26, 2011

Fractionally-Cloudy Days

Yesterday we looked at the use of percentages in predicting the weather. Today I'll quickly run over how we can use fractions when talking about weather conditions. We teach both fractions and percentages in our Excel Math curriculum.

Do you like clouds? I like scattered clouds, and partly-cloudy days. Most of the time.

Beautiful New Mexico day with scattered clouds 

But not always, especially if we are flying somewhere.

This Greek cloud over Athens made us use airsickness bags ...

CLOUD: a visible aggregate of minute water droplets or ice particles in the atmosphere above the Earth's surface.

There are special weather words associated with cloudy days. Weather forecasters notice how many 8ths of the sky covered with cloud, then use their special terms:
  • 0/8ths  – Clear or Sunny
  • 1/8th to 2/8ths – Mostly Sunny
  • 2/8ths to 3/8ths – Scattered Clouds
  • 3/8ths to 5/8ths  – Partly Cloudy
  • 6/8ths to 7/8ths – Mostly or Considerable Clouds
  • 8/8ths – Cloudy
Some places in the world have dramatic clouds and others do not. I will give you a couple examples so you can see what I mean.

 Interesting Swedish clouds

 Boring San Diego clouds

San Diego doesn't often get interesting clouds. We are so close to the ocean that we tend to get a marine layer pushed onto us instead.

MARINE PUSH: A replacement of the current air mass with air from off the ocean. Temperatures are much cooler and relative humidities are much higher.

Local residents call this June Gloom. If you come here on vacation to visit the Zoo or Sea World, you are likely (57% of the time) to see grey gloomy days instead of sunshine.

Our sunniest month is actually November. In an average year, San Diego has 68% sunshine, 3055 hours of sun and 146 clear days.

(% Sunshine = percentage of time between sunrise and sunset that sun reaches the earth's surface; Clear Day = when clouds cover less than one-third of the sky on average)

Go here to read about the San Diego Weather Year for yourself.
My favorite partly-cloudy San Diego sky, from the breakfast table at sunrise

    Wednesday, May 25, 2011

    Probable Percentage of Precipitation

    In our never-ending quest to find a way to use our elementary school math skills, let's start today with a quote:  "40% chance of rain tonight."

    What does a 40% chance of rain mean?

    Will it rain 40 percent of of the time? ... will it rain over 40 percent of the area? ... will we receive 40% of what has been forecast?

    RAIN: precipitation that falls to earth in drops more than 0.5 mm in diameter.

    The Probability of Precipitation (PoP) as defined by the US National Weather Service, is the likelihood, expressed as a percent, of a measurable precipitation event (1/100th of an inch) at a grid point during the indicated valid period.

    How do forecasters arrive at this esoteric prediction?

    Mathematically, PoP is defined as follows:

    PoP = C x A 

    C = confidence factor that precipitation will occur somewhere in the forecast area
    (If C = 1 it is certain to rain; if C=0 it will never rain, and if C is in-between, it might rain)

    A = percentage of the area that will receive measurable precipitation, if it occurs at all.

    A 40% forecast may mean the forecaster believes precipitation will surely occur (100%  confidence), and he/she is expressing how much of the area will receive measurable rain (more than 1/100th of an inch, falling in drops greater than .5 mm diameter).

    PoP = 1 x .4 which equals .4 or 40%

    Alternatively, a forecaster might express degree of confidence and area coverage. If he's 50% sure that precipitation will occur, and if it does occur, it will produce measurable rain over 80% of the area, the PoP (chance of rain) is 40%.

    PoP = .5 x .8 which equals .4 or 40%

    The forecast says on average, for any point within the specified area, during the 12 hour time period, the chance that measurable rain will occur is 40 percent.

    In addition to the forecast, there are special "weatherman" terms triggered by PoP percentages:
    • 0% - 10% – No mention of precipitation
    • 10% - 30% – Isolated or slight chance
    • 30% - 40% – Widely scattered or chance
    • 40% - 60% – Scattered or chance
    • 60% - 80% – Numerous or likely
    • 80% - 100% – Rain, plus modifiers like showers or thunderstorms

    Don't you hate rain when you are camping?

    I hope you learned about fractions and percentages when you were in elementary school. You need them to understand the weather. We cover this subject extensively in our Excel Math curriculum.

    Go to the National Weather Service's 2000-word glossary to learn more about their jargon.