The library of Eratosthenes

Adelaide

Friday 21 March 2008 by perbosc


Noon-day Project March 2008
Matthew and Peter Sowerbutts Adelaide South Australia

 Introduction

Hello my name is Matthew. I am 9 and I live in Adelaide South Australia. It is very hot right now and at the moment we are having a drought.


Longitude is 138 degrees 39.7 minutes East
Latitude is 34 degrees 51.7 minutes South


I am homeschooled with my 3 brothers- Peter 12, Christopher 7 and Anthony 4. I have an older brother and sister who go to school.

Sydney is one of the best known cities in Australia.
Adelaide is smaller but is also a great place to live. We have hundreds of Fairy Penguins on Granite Island. In the evening they come out of the sea and walk across the paths to get to their nests.

 During the first week...

... of the project we did several things to get ready.

1. We read the book The Librarian Who Measured the Earth. We learned how Eratosthenes used shadows and angles to measure the circumference of the earth more than two thousand years ago.

2. We made a shadow clock. We used a pencil standing upright on a piece of paper. We placed it outside in the sun and recorded the length of the shadow cast by the pencil. We measured the length each half hour for a few hours each side of noon. By finding the shortest shadow we discovered the direction of North and the approximate time of local noon. This turned out to be 1.20pm.

3. We looked up on the internet and found some useful information
(a) Our exact longitude and latitude for Windsor Gardens South Australia-
Latitude 34.86° South
Longitude138.66° East
(b) Listing of exact times of local noon for Adelaide for every day of the year. 1.23pm was the exact time for March 21st
(c) That between each degree of Latitude there was approximately 111km.
(d) That on March the 21st the angle of the sun was zero at the equator.

4. We got our equipment ready
Metre Ruler
Library bookend to keep our ruler at 90°
Tape to attach ruler to bookend
Tape measure
Clock
Paper for shadow to fall on

 On March 21st

We went outside and measured the shadow length of the metre ruler every minute for about 5 mins each side of local noon (1.23pm). We used a measuring tape with millimeter divisions. The measurement was difficult to get exactly due to the shadow being fuzzy at the end and the ruler wobbling in the slightest breeze. We did our best and got 72.5 cm.

 Later...

1. We read the book Sir Cumference and the Great Knight of Angleland and practiced measuring angles with a protractor.

2. We got a big piece of paper and drew in the metre ruler and the shadow. Then we had to join them up to make a triangle. This was a bit difficult as we didn’t have anything long enough so we used a long board and the metre ruler. We measured the angle between the top of the ruler and the line joining the top of the ruler to the end of the shadow. We used a protractor with the smallest measure being one degree. We got 36 ° as our sun angle.

3. Circumference measurement.
Then we partnered with the equator as we knew the sun angle there was zero. We used our latitude 34.86 ° South and our knowledge that we could multiply this by 111km to find our distance from the equator. We calculated approximately 3900kms.
This was the distance of our wedge. As our sun angle was 36 ° that made 10 wedges to make up a full earth of 360 °. Multiplying 3900 by 10 gave a circumference of 39000kms. This was slightly different from the actual circumference of about 40,000kms but quite good considering the accuracy of our measuring equipment

4. We looked at everyone else’s data on the Noon-day site. We got out our world map and using the latitude and longitude measures we marked all their positions.
We choose 3 other groups to partner with:
Xiamen International School China
College Antonin Perbosc France
Arsenault Homeschool USA
To work out the size of each wedge we added our degrees of latitude together and multiplied by 111km. This gave the distance as if we had moved each of the other schools across to our longitude and then measured directly North.
To work out the number of wedges we added our 2 sun angles together and divided it into 360.
We then calculated the circumference by multiplying the distance of each wedge by the number of wedges.

 Circumference results:

With
Xiamen International School China 40,817km
College Antonin Perbosc France 39,456km
Arsenault Homeschool USA 39,095km


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