# Ely, Nevada and its surrounding area

I discovered Ely, Nevada’s homepage recently and particularly enjoyed it: Ely, Nevada Home Page., but especially for the sentence (near the bottom of the page): “Centrally located in the intermountain west, Ely and the surrounding area contains a population of over 6 million people within a 500 mile radius.”

I loved the humor and creativity evident in that sentence. And then I thought, “What questions could I ask to make sense of this statement? How could I share this statement with a math class?” I considered the questions:

• In order to engage in answering any of the questions below, what tools can I use?
• Is there an online tool that, given a map, would create the circle for me? Is there a tool that would add up the populations for me?
• Creating the circle (if using the map, figuring out scales, etc. is important):
• Get a map of US (either a folded map or print out a map from Google Maps) and a compass, measure the size of “500 miles” and use the compass to create a circle
• Get a digital map of US and use GeoGebra to draw a circle (depending on how precise I want)
• Finding populations:
• How precise should I be?
• Should I choose the largest cities, and look up the metro populations? What is my “cut-off point” for city size?
• How far would I be under-estimating, if I don’t count all of the smaller towns and cities?
• What does “surrounding area” really mean?
• If I draw my intuitive sense of what “surrounding area” means on a map, how big of an area does it include? Do my classmates have similar or different ideas about the size of “surrounding area”?
• How big of a radius should I use to include the whole US? Where would I center it? How much of Canada, Mexico, or other countries would be included?
• How big is a region with a 500-mile radius?
• What cities / metro areas are included in the 500-mile radius circle centered at Ely?
• Could they have chosen a smaller radius and still included an impressive population?
• Are there particular cities they wanted to include that inspired their choice of 500 miles?
• Where I am now (in East Lansing, MI):
• If I created a circular region of radius 500 miles centered on East Lansing
• How many people would be contained in that region?
• What cities would be contained in that region?
• If I wanted to include a population of 6 million people, how large should the radius be, if I centered the circle on East Lansing?

I will try to engage in this task when I have more time…

In order to engage in answering any of the questions below, what tools can I use?

• Is there an online tool that, given a map, would create the circle for me?
• Is there a tool that would add up the populations for me?
• Finding populations:
• How precise should I be?
• Should I choose the largest cities, and look up the metro populations? What is my “cut-off point” for city size?
• How far would I be under-estimating, if I don’t count all of the smaller towns and cities?

How big is a region with a 500-mile radius?

• What cities / metro areas are included in the 500-mile radius circle centered at Ely? The map shows some large cities are: Salt Lake, Ogden, Provo, Las Vegas, Reno, Phoenix, Los Angeles, San Jose, San Francisco, Fresno, Sacramento, San Diego, Tijuana (Mexico), Boise, Idaho Falls
• I’m going to estimate the population. I notice that all of Nevada (2.839 million) and Utah (2.943 million) are contained. So that’s already about 6 million people! Most of California is contained, except for a tiny piece in the northwest that includes Crescent and Eureka, and California has population 38.8 million – let’s be conservative and knock off about 8.8 million for that tiny corner and we still have 36 million contained. The Phoenix metro area adds about 3 million. Tijuana adds about 1.483 million. Boise (0.616) and Idaho Falls (0.130) add a little less than a million. I could keep adding on, but a low estimate is still over 40 million.
• I found that the same site I used to create the circle also will estimate population within the radius, and it says “The estimated population in the defined area is 49,997,320.”
• Could they have chosen a smaller radius and still included an impressive population?
• I’m going to guesstimate and say 250-300 mile radius would probably still include 6 million people.
• Let me test my conjecture. (Note that I needed to reset the site before changing the radius, or it told me the same population as above.)  I entered 250 miles and was told “The estimated population in the defined area is 4,331,681.”  300 miles was closer with 5,438,487, and 315 was slightly more than 6 million with 6,396,013.
• Are there particular cities they wanted to include that inspired their choice of 500 miles?
• I’m guessing it is cool to say that San Fran and other California cities are “in the surrounding area.”

Where I am now (in East Lansing, MI):

If I created a circular region of radius 500 miles centered on East Lansing

• How many people would be contained in that region? Well, it includes all of Michigan (9.91), Wisconsin (5.758), Illinois (12.88), Indiana (6.597), Ohio (11.59), West Virginia (1.85), Washington, D.C. (0.658), and Kentucky (4.413). So, as a low estimate, a 500-mile region would include a population of at least 53.656 million.
• I was much, much too low! With the population finder, I found  the estimated population in the defined area is 101,594,400
• If I wanted to include a population of 6 million people, how large should the radius be, if I centered the circle on East Lansing? I conjecture 90 miles. Metro areas for Detroit (3.734), Lansing (0.464), Grand Rapids-Muskegon-Holland (1.321), Kalamazoo (0.326), and Flint (0.425) would be just over 6 million.

I’m really under-estimating though, because I choose to balance time over precision (time of looking up populations), but the radius around East Lansing of 90 miles would definitely include 6 million people. Using the population tool, I found that 75 miles radius would include 6,795,008 people.