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## A Response to The Oklahoma Land Problem

It is always great when someone provides feedback to MathNEXUS items. For example, consider the following feedback to last week's MathLint...for which Bob deserves a HIGH FIVE!

Ahoy Mathemagicians,

MathNEXUS is a weekly treasure. We almost always find something interesting. This week we were titillated by Land For Sale.

Here's the problem: The federal government was selling some land near Beaver, Oklahoma. Which of these lots would you be interested in?

• Parcel A: 1 mile long and 2.64 feet wide
• Parcel B: 2.5 miles long and 50 feet wide
My questions are several. First, if you bought Parcel A, what could you do with it? You could not build anything on it, as such requires it be more than 10 feet wide to meet frontage rules.

Second, I can imagine building a small house at one end of Parcel B, with a 2.5 mile long lawn in front of it...and a 2.5 mile winding driveway! [Suppose that the driveway is in the shape of a sine function. How long is it? B&G]

And third, what is the acreage of each plot?

We would love to own Parcel B. It is about 4.0 kilometers (4000 meters) long and 15 meters wide. We would buy it and build a scale model of the Solar System, even including dwarf planet Pluto. We would put the Sun at one end and the planets at scale model distances from the Sun with a kiosk describing each planet in great detail.

Scale: 100 meters : 1 AU (astronomical unit)

Here are the distances of the planets from the Sun and their distances from the scale model Sun in our model. Please check our arithmetic.

Planet: Distance (AU) = Scale Distance (meters)
Mercury: 0.387 AU = 38.7 m
Venus: 0.723 AU = 72.3 m
Earth: 1.000 AU = 100.0 m
Mars: 1.524 AU = 152.4 m
Asteroids: 2.8 AU = 280 m (Ceres & Pallas)
Jupiter: 5.204 AU = 520.4 m
Saturn: 9.582 AU = 958.2 m
Uranus: 19.201 AU = 1920.1 m
Neptune: 30.047 AU = 3004.7 m
Pluto: 39.482 AU = 3948.2 m

Imagine walking or biking along our scale model on a nice morning. Bring a lunch, enjoy it at Pluto, and then stroll back to the Sun. Eight kilometers of exercise and learning about the Solar System.

Oops, almost forgot. The area of this 4000 meter by 15 meter parcel is 60,000 square meters = 6 hectares.

What about Parcel A? It is about 1.6 kilometers (1600 meters) long and 0.80 meter wide. These possibilities popped into mind:

1. Paul Bunyan's one-lane bowling alley
2. World's longest one-lane swimming pool