Sunday, February 07, 2010

Sexagesimal or "How I fell in love with latitude (again)"

I would like to thank the Babylonians for making life so interesting. You see, they used a base 60 system in their calculations and measurements. Sixty is a highly composite number, having 12 factors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60). With so many factors, many fractions of sexagesimal numbers are simple. For example, an hour can be divided evenly into segments of 30 minutes, 20 minutes, 15 minutes, etc. Sixty is the smallest number divisible by every number from 1 to 6. I would also like to thank the earth for being spherical. Many civilizations observed and accurately recorded the celestial passage of time. Those lovely Babylonians figured out that a circle that be neatly divided in 360 neat degrees. To get a circle to neatly divide out to include all factors 1-7, it would have to have 2520 degrees--I always knew 7s were pesky!

Anyway, this is all very interesting because of what it has to do with latitude, longitude and navigation. We recently started our hunt for the Journey North Mystery Class sites. By recording the sunrise/sunset and photoperiod data for 11 sites worldwide, we (along with a group of friends) will try to pinpoint the mystery class locations.

We have been having so much fun with the book Geography Wizardry for Kids. We estimated our latitude using a globe and then a flat map and then we set about making various instruments to measure our latitude.

The latitude finder from the book went as follows:

Supply list: Heavy cardboard at least 13 inches long, ruler or yardstick, pencil, scissors, two-pronged paper fastener, protractor, piece of string at least 18 inches long, a nail.

1. From corner of the cardboard, use the ruler to measure 13 inches down the side. With a pencil, make a mark at that point. From the same corner, measure 13 inches towards the other edge and make a mark. Use a ruler to draw a straight line between the two marks.

2. Cut out the triangle.

3. Draw lines 1 inch in from the corner, parallel to each side (from the right angle).

4. Where those lines intersect, make a small hole with the nail.

5. Set the protractor on our latitude finder so that the center mark is over the hole you have punched. race the edge of the protractor and mark the first 60 degrees. Draw lines outward from the center mark at the degree marks for 0, 10, 20, 30, 40, 50 and 60 degrees. Draw dots for the individual degrees (1-9) in between.

6. Insert a two-pronged paper fastener through the hole in the triangle. Tie one end of the string under the head of the paper fastener, attach the nail as a weight.

How to use your contraption:

1. Find the North Star
2. Stand at a level place and hold your latitude finer to your eye at the level of the paper fastener. Have a friend check that the bottom of the finder is parallel to the ground.
3. Close one eye, and pull the string taut. Hold the string so that it points to the North Star.
4. Have your helper make a small mark with a pencil at the point that the string crosses the finder.
5. Hold a ruler between the mark and the protractor markings and find the degree of latitude.
6. Take three sightings and compute your average (our eyes can be a bit wobbly).

Because the latitude finder was so fun to make and so simple, we decided to try out hand at making a more traditional Sextant. We have a tiny one some friends brought us from Greece.

We looked at it and at our cardboard latitude finder and came up with this fine design:

It is a tube with two sets of cross-hairs for spotting, a protractor to measure degrees and a pendulum that we are able to twist down when we have taken out sighting. It was incredibly accurate and easier to use than the latitude finder. We also found gobs of directions online for making sextants, our two favorites being this one(FANCY), and this one (also kind of fancy but involves Legos again).

Ours was much simpler and very accurate. If you build one, send us a picture and a description.

We ended the night watching NOVA: Lost at Sea: The Search for Longitude which was based on Dava Sobel's book Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time, a book we read aloud a few years ago and we are still talking about.

We estimate dour latitude using a globe, a flat map and and the observations from our two instruments. Then we went online and found our latitude with good ol' GPS. Our homemade sextant and the flat map had given us the most accurate estimates. None of our methods were too far off the mark--of course when navigating at see, being just a little of the mark can be disastrous.

Finding one's place in the world, literally and figuratively is what life is all about. Delving into the questions and calculations about latitude, longitude, maps, astronomy, math--it has really caught our imagination and we can't wait for more!


Polly said...

How much fun!!! We've been enjoying the Journey North project, too. We're definitely not as thorough, but you've inspired us!!
Polly, Hannah, Elly, and Bob

denise said...

fun! we are doing that project too. we have spent a few months doing fun stuff with telescope, GPS, long/lat/math and all that. boys are younger, but love love love numbers and figuring that stuff out. :)

cool post!

Frank said...

Very cool. I remember reading a wonderful essay by Isaac Asimov in the 60s when I was taking celestial navigation. It's a fascinating subject.

Have fun!