Spring Break Prep, GPS, and Latitude Longitude Grid

After working with coordinate grids and dilations over the last two weeks, I could think of no better way to take the children on a long awaited Spring Break then go to Oh the Places You Go--Where the Mathlete Families Would Have Traveled this Year.

I received responses from over 100 families and some of their destinations included cities in every continent except Antarctica. I researched the latitude and longitude coordinates of each and attempted to introduce the children to this location system.

Boy and Girl Scout Motto is "Be Prepared.” Mathematicians and chess players always think ahead. Children should appreciate the planning parents do to ensure a successful vacation.

Let's go on vacation for Spring Break, but first ...

1. Schedule Flights at times that give you the most time away and less time in airports.

2. Seats on plane are together and near the front of the plane; not next to a smelly bathroom.

3. Update passport if you are traveling out of the country (expiration date must be at least 6 months after you expect to return). You may need a visa as well to certain countries.

4. Call your Bank to let them know where you are traveling so they will not block your credit or debit card when you need it most.

5. Foreign Currency should be obtained in advance as exchanging money at the airport or in the destination country can be expensive. 

6. Research and learn History of your destination so you know some of the key places you want to visit and gain respect for the culture; some sites may require advanced reservations. Download maps on your phone should you not have good wifi (I use CityMaps2Go Offline Maps).

7. Hotel or AirBnb should be centrally located to where you expect to be doing most of your site seeing. 

8. Transportation from airport to hotel and to some key sites should be organized in advance. Renting a car in advance can save a lot of money and agencies often run out of cars.

9. GEAR: try to think of what you will need when you are there. Sunscreen can be purchased at your destination, but it is expensive. Books or  audio for tablets. Games such as chess, sudoko, playing cards, etc. Blanket, pillow, or stuffed animal if you need them to fall asleep (also, beware that you risk losing these important artifacts while traveling). Sports gear (snorkel and mask, tennis ball to play catch) can be important or can be rented where you go (I usually bring my kitesurfing gear but in Columbia in February, I rented on the beach).

10. Pack lightly. Check the weather so you know what kind of clothes to bring (over-prepare on warmth; you can always shed a layer). Bring older comfortable shoes, a hat, and sunglasses you won't mind losing. Leave room in your luggage for buying a souvenirs or two (although souvenirs are often a waste of money; however, they do support the local economy). If you go to a poor country, bring small gifts like bouncy balls or action figures you don't use anymore to give away to children.

11. Cell phones are a safety precaution but can be expensive if in a different country. International plans are inexpensive if organized in advance. Cameras are usually integrated into phone (make sure you have space on your hard drive or save on the Cloud). Global Positioning System (GPS) is a great way to find points of interest and prevent getting lost. 

Global Positioning System (GPS):

Our ancestors had to go to pretty extreme measures to keep from getting lost. They erected monumental landmarks, laboriously drafted detailed maps and learned to read the stars in the night sky.

Things are much, much easier today. Most electronic devices (cell phone, watch, tablets) have a GPS receiver and a clear view of the sky, you'll never be lost again.

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GPS is actually a constellation of 27 Earth-orbiting satellites (24 in operation and three extras in case one fails). The U.S. military developed and implemented this satellite network as a military navigation system, but soon opened it up to everybody else. Each of these 3,000- to 4,000-pound solar-powered satellites circles the globe at about 12,000 miles altitude, making two complete rotations every day. The orbits are arranged so that at any time, anywhere on Earth, there are at least four satellites "visible" in the sky. A GPS receiver's job is to locate four or more of these satellites, figure out the distance to each, and use this information to deduce its own location. This operation is based on a simple mathematical principle called trilateration (or triangulation). Trilateration in three-dimensional space can be a little tricky, so we'll start with an explanation of simple two-dimensional trilateration.

Imagine you are somewhere in the United States and you are TOTALLY lost -- for whatever reason, you have absolutely no clue where you are. You find a friendly local and ask, "Where am I?" He says, "You are 625 miles from Boise, Idaho.” This is a nice, hard fact, but it is not particularly useful by itself. You could be anywhere on a circle around Boise that has a radius of 625 miles.

You ask somebody else where you are, and she says, "You are 690 miles from Minneapolis, Minnesota." Now you're getting somewhere. If you combine this information with the Boise information, you have two circles that intersect. You now know that you must be at one of these two intersection points, if you are 625 miles from Boise and 690 miles from Minneapolis.

If a third person tells you that you are 615 miles from Tucson, Arizona, you can eliminate one of the possibilities, because the third circle will only intersect with one of these points. You now know exactly where you are -- Denver, Colorado.

This same concept works in three-dimensional space, as well, but you're dealing with spheres instead of circles. The GPS receiver figures both of these things out by analyzing high-frequency, low-power radio signals from the GPS satellites. Radio waves are electromagnetic energy, which means they travel at the speed of light (about 186,000 miles per second in a vacuum). The receiver can figure out how far the signal has traveled by timing how long it took the signal to arrive. 

BUT HOW DOES GPS RECORD YOUR LOCATION?

A Cartesian plane with latitude as the horizontal axis with zero degrees at the equator and longitude as the vertical axis with zero degrees at the Prime Meridian which goes through Greenwich, England. When recording a location, first record the latitude as north or south, then record the longitude as east or west. Latitude goes from 90 degrees north to 90 degrees south. Longitude goes from 180 degrees west to 180 degrees east (both of which are the same vertical line called the International Date Line, on the opposite side of the Prime Meridian).

I gave the children several exercises where they could practice finding locations or recording the coordinates of their favorite places. The last challenge was to find each of the 50 destinations of Mathlete families on the world map using latitude and longitude.