Eratosthenes Experiment
A Worldwide Science and Math Experiment
March 20, 2012

Dates to remember on this project: Project Summary:

This fun one day project allows students from all over the globe to calculate the circumference of the Earth by measuring the shadow of the sun, then using that measurement in a simple equation. Students and classes are encouraged to share their results with others by completing an experiment report form.

You may view the March 2012 experimental results of participating students and classes. March 1997, September 1997, March 1998, September 1998, March 1999, September 1999, March 2000, September 2000, March 2001, September 2001, March 2002, September 2002, March 2003, September 2003, March 2004, September 2004, March 2005, September 2005, March 2006, September 2006, March 2007, September 2007, March 2008, September 2008, March 2009, September 2009, March 2010 September 2010, March 2011, and September 2011 experimental results are also available via the WWW.


			March 2012 Experiment Summary

  School                Lat   Measured  Calculated Circumference

Felix Festa MS, NY[1]	41.124	60	27,438    km / 17,049.18 mi
Fayetteville CC, NC[5]	35.067  40	35,064    km / 21,787.76 mi
Felix Festa MS, NY[2]	41.124	45	36,584    km / 22,732.24 mi
James River HS, VA	37.55	40	37,575    km / 23,348.02 mi
Fayetteville CC, NC[19] 35.067  37	37,907    km / 23,554.32 mi
Fayetteville CC, NC[8]  35.067  37	37,913.5  km / 23,558.36 mi
Fayetteville CC, NC[20] 35.067  35.6	38,708    km / 24,052.04 mi
Fayetteville CC, NC[7] 111.12   36	38,960    km / 24,208.62 mi
Fayetteville CC, NC[3]	35.07   40	38,974.3  km / 24,217.51 mi
Fayetteville CC, NC[9]	35.067  35.73	39,261.13 km / 24,395.74 mi
Fayetteville CC, NC[9]	35.067  35.6	39,404    km / 24,484.51 mi
Bjerget ES, Denmark[12]	57.11	57.69	39,703    km / 24,670.30 mi
Bjerget ES, Denmark[14]	57.11	57.59	39,722    km / 24,682.11 mi
Bjerget ES, Denmark[15]	57.11	57.54	39,759    km / 24,705.10 mi
Richford Jr/Sr HS, VT   44.994  45.20	39,830.89 km / 24,749.77 mi
Bjerget ES, Denmark[13]	57.11	57.26	39,956    km / 24,827.51 mi
Fayetteville CC, NC[17]	35.07   35	40,001.14 km / 24,855.56 mi
=>Earth's Polar Circumference           40,008    km / 24,859.82 mi<=
Dryden HS, Canada[10]	49' 47	49.8	40,019    km / 24,866.66 mi
Fayetteville CC, NC[4]	35.07   35	40,073    km / 24,900.21 mi
Fayetteville CC, NC[6]	35.067  35	40,083.43 km / 24,906.69 mi
Dryden HS, Canada[22]	49.78	49.4	40,343.32 km / 24,866.66 mi
Dryden HS, Canada[11]	49' 47	48.544	41,054.71 km / 25,510.22 mi
Fayetteville CC, NC[18]	35.067  34	41,252    km / 25,632.81 mi
Fayetteville CC, NC[16]	35.067  33	42,501.82 km / 26,409.41 mi
Dryden HS, Canada[21]	49' 47	40	49,824    km / 20,959.20 mi


[1] Kaitlyn, Alanna, Shawna, Payton
[2] Caroline, Danielle, Josh
[3] Charles
[4] Rory, Jorge, Duwayne, Michael, Arthur, Irishmr, Clint, Ifeyinwa, Patrick
[5] Nicholas, CHZ711024, Tyler, Christopher, Dr. T Maher, James
[6] Joshua
[7] Gregory, Grenade31a, Allen
[8] Lawrence
[9] Zeus, Nakiya
[10] Michael and Lacey
[11] Adrian, Brenden, Will
[12] Jakob,Rikke, Carina
[13] Casper, Ida
[14] Emil, Markus, Jakob L
[15] Regitse, Tea, Plik
[16] Samantha, newbled1738
[17] Gerald P.
[18] Greg
[19] Justin
[20] Josh
[21] Charles
[22] Geoff, Ethan, Brittany, Jai, Kelsey, Dana


IES ITALICA, Spain
N.A.S.Inter college,Meerut,UP,India


		     September 2011 Experiment Summary

  School                Lat   Measured  Calculated Circumference

Cole Ridge HS, CO[38]	39 37	74	21,381.1  km / 13,285.6  mi
Fayetteville TCC,NC[30]	35.07	45	31,117.03 km / 19,335.23 mi
Fayetteville TCC,NC[9]	35.07	45	31,118.08 km / 19,335.88 mi
Fayetteville TCC,NC[10]	35.07	45	31,142.16 km / 19,350.84 mi
Fayetteville TCC,NC[3]	35.07	45	31,173.6  km / 19,370.38 mi
Fayetteville TCC,NC[8]	35.07	45	31,173.6  km / 19,370.38 mi
Fayetteville TCC,NC[13]	35.07	45	31,173.6  km / 19,370.38 mi
Fayetteville TCC,NC[17]	35.07	45	31,173.6  km / 19,370.38 mi
UNC Wilmington, NC	34.23	37	37,298.50 km / 23,176.22 mi
Cole Ridge HS, CO[34]	39 37	48.36	37,997    km / 23,610.24 mi
Cole Ridge HS, CO[24]	39 37	41.5	38,125    km / 23,689.78 mi
Belle Vernon HS, PA	40.18	42	38,274.17 km / 23,782.47 mi
Dryden HS, Canada[21]	49.78	51.78	38,656.11 km / 24,019.79 mi
Fayetteville TCC,NC[1]	35.07	30	38,724    km / 24,061.98 mi
Fayetteville TCC,NC[6]	35.07	30	38,924.72 km / 24,186.7  mi
East HS, MO [15]	39 6	51.9	39,000    km / 24,233.48 mi
Cole Ridge HS, CO[25]	39 33	40.39	39,173    km / 24,340.98 mi
East HS, MO [19]	39 6	50	39,200    km / 24,357.75 mi
Cole Ridge HS, CO[35]	39 33	40.2	39,358    km / 24,455.93 mi
Harry M Arndt MS, NC	35 46	36	39,600.64 km / 24,606.7  mi
Cole Ridge HS, CO[28]	39 33	39.66	39,894    km / 24,788.98 mi
Fayetteville TCC,NC[5]	35.07	45	39,960    km / 24,829.99 mi
Riverbend Academy, FL	29.251	29	39,981.85 km / 24,843.57 mi
=>Earth's Polar Circumference           40,008    km / 24,859.82 mi<=
Fayetteville TCC,NC[16]	35.07	45	40,010.98 km / 24,861.67 mi
Cole Ridge HS, CO[27]	39 33	39.54	40,015.51 km / 24,864.49 mi
Cole Ridge HS, CO[29]	39 33	39.54	40,034    km / 24,875.98 mi
Fayetteville TCC,NC[2]	35.07	35	40,036.8  km / 24,877.72 mi
Fayetteville TCC,NC[11]	35.07	35	40,114.3  km / 24,925.87 mi
Galesburg HS, IL	40.94	40	40,500    km / 25,165.53 mi
Cole Ridge HS, CO[36]	39 33	39.05	40,517.29 km / 25,176.28 mi
Fayetteville TCC,NC[4]	35.07	34.5	40,617.03 km / 25,238.25 mi
Pine Island ES, FL	26 37	26	40,734.10 km / 25,311    mi
Fayetteville TCC,NC[12]	35.07	42	40,834.29 km / 25,373.25 mi
Bjerget ES, Denmark	57.06	55.9	40,860    km / 25,389.23 mi
Cole Ridge HS, CO[26]	39 33	38.7	40,883.7  km / 25,403.95 mi
East HS, MO [14]	39 6	51.9	40,900    km / 25,414.08 mi
East HS, MO [18]	39 6	52	41,200    km / 25,600.49 mi
Cole Ridge HS, CO[33]	39 33	33.7	41,582.4  km / 25,838.11 mi
East HS, MO [20]	39 6	52	41,900    km / 26,035.45 mi
Cole Ridge HS, CO[32]	39 33	37.73	41,930    km / 26,054.1  mi
Howell HS, NJ		40.2	40	41,958    km / 26,071.49 mi
Cole Ridge HS, CO[31]	39 33	37.45	42,248.33 km / 26,251.9  mi
Cole Ridge HS, CO[39]	39 33	37	42,762    km / 26,571.08 mi
Cole Ridge HS, CO[37]	39 33	37	43,229.50 km / 26,861.57 mi
Fayetteville TCC,NC[7]	35.07	32	43,790.06 km / 27,209.88 mi
Dryden HS, Canada[22]	49.78	39.6	53,450    km / 33,212.29 mi

[1] Veronica
[2] Patricia
[3] Tovey C - Bad equator distance: 9002 km; recalculated using 3896.7 km
[4] Lindsay, Tara
[5] Wanda 
[6] Marcella
[7] Emma, Lashunda, Eratosthenes
[8] Roosevelt - Bad equator distance: 9528 km; recalculated using 3896.7 km
[9] Sherlene 
[10] Mandy
[11] Lauran
[12] Shani
[13] Angela -  Bad equator distance: 38,924.649 km; recalculated using 3896.7 km
[14] Team blue
[15] Team AAAS
[16] Amy
[17] Tammy -  Bad equator distance: 9002 km; recalculated using 3896.7 km
[18] Team 1
[19] Team 2
[20] Team 3
[21] Alex, Caine, Ethan, Ryan
[22] Marion, Kara, Mark, Phil
[23] #1
[24] tuyet
[25] team
[26] Team Legit
[27] Team We Tried
[28] Los Frijoles
[29] Team Name
[30] Roosevelt
[31] XXL's
[32] BF Changs
[33] Harvey's
[34] The Greek Wannabe's
[35] Awesomesauce on 27
[36] OliviannAustinators
[37] BAMF's
[38] What
[39] Barbies


AGS - Alssundgymnasiet Snderborg, Denmark
Central HS District of Westosha, WI
Frewsburg Central HS, NY
Grace Christian Academy, Taiwan
Highland HS, AR
The Planetary Society/FaCE CA
Turkeyfoot Valley HS, PA
Warwick Valley HS, NY



		     March 2011 Experiment Summary

  School                Lat   Measured  Calculated Circumference

Parkwood MS, NC		34.8979	45	31,077.54 km / 19,310.69 mi
FICC, NC[12]		36.07	44.0	31,877.50 km / 19,807.76 mi
Cole Ridge HS, CO[17]	39.55	46.8	33,869.00 km / 21,045.22 mi
FICC, NC[10]		36.07	40.0	35,013.00 km / 21,756.07 mi
FICC, NC[5]		36.07	39.0	36,034.09 km / 22,390.55 mi
Cole Ridge HS, CO[20]	39.55	41.82	37,902.00 km / 23,551.21 mi
Cole Ridge HS, CO[18]	39.55	41.6	38,102.80 km / 23,675.98 mi
Bjerget ES, DENMARK[1]  57 06'	58.5	39,068.00 km / 24,275.73 mi
Bjerget ES, DENMARK[2]	57 06'	58.3	39,181.00 km / 24,345.95 mi
Cole Ridge HS, CO[14]	39.55	39.55	39,250.00 km / 24,388.82 mi
Bjerget ES, DENMARK[3]	57 06'	57.9	39,442.00 km / 24,508.12 mi
Cole Ridge HS, CO[19]	39.55	40.035	39,592.16 km / 24,601.43 mi
FICC, NC[8]		36.07	40.0	39,633.24 km / 24,626.95 mi
Cole Ridge HS, CO[25]	39.55	39.8	39,844.20 km / 24,758.04 mi
APerbosc College,FRANCE	44 08'	44 16'	39,882.00 km / 24,781.53 mi
=>Earth's Polar Circumference           40,008    km / 24,859.82 mi<=
W Essex HS, NJ		41	--	--	     / --          **
FICC, NC[7]		36.07	38.0	40,009.00 km / 24,860.44 mi
Cole Ridge HS, CO[21]	39.55	40.183	40,027.27 km / 24,871.79 mi
Cole Ridge HS, CO[15]	39.55	50.2	40,074.27 km / 24,901.00 mi
FICC, NC[13]		36.07	35.0	40,076.00 km / 24,902.07 mi
Cole Ridge HS, CO[24]	39.55	39.47	40,149.00 km / 24,947.43 mi
IntSchool Paris, France	48 49'	48	40,688.69 km / 25,282.78 mi*
Bjerget ES, DENMARK[4]	57 06'	56	40,786.00 km / 25,343.25 mi
Cole Ridge HS, CO[22]	39.55	38.7	40,905.00 km / 25,417.19 mi
FICC, NC[9]		36.07	34.0	41,333.00 km / 25,683.14 mi
Cole Ridge HS, CO[16]	39.55	36.625	42,617.82 km / 26,481.49 mi
Cole Ridge HS, CO[23]	39.55	36.82	43,049.43 km / 26,749.68 mi

*Corrected latitude and distance to Equator
**Unable to complete experiment because of cloud cover

Bjerget ES, DENMARK[1] - Kasper
Bjerget ES, DENMARK[2] - Plik
Bjerget ES, DENMARK[3] - Annika og Sebastian
Bjerget ES, DENMARK[4] - Joachim
FICC, NC[5]	       - Jeremy, Brook, Felton, Ronnie
FICC, NC[6]            - Michael		Bad angle/ Equator distance
FICC, NC[7]            - Jackie, William
FICC, NC[8]            - David
FICC, NC[9]            - Robert, Henry
FICC, NC[10]           - Briana
FICC, NC[11]           - Melissa		Not at solar noon
FICC, NC[12]           - Ernest, Roland, David
FICC, NC[13]           - Derek
Cole Ridge HS, CO[14]  - Powderpuff Girls, AA Participants
Cole Ridge HS, CO[15]  - Fantastic Four
Cole Ridge HS, CO[16]  - Michael, The Shockers
Cole Ridge HS, CO[17]  - The Avengers
Cole Ridge HS, CO[18]  - CACK
Cole Ridge HS, CO[19]  - John, Sami, Lena, Kathleen, Kelvin
Cole Ridge HS, CO[20]  - McLovin
Cole Ridge HS, CO[21]  - ATTWF
Cole Ridge HS, CO[22]  - NoNames
Cole Ridge HS, CO[23]  - Ty, Trevor, Zoe, Si, Alicia
Cole Ridge HS, CO[24]  - Kinsey, Cameron, Zach, Snoder
Cole Ridge HS, CO[25]  - Chelsie, Jessica, Brini, Amanda


Bay Point MS, FL
Caterham, UK
Felix Festa MS, NY
IIS-S "G. La Pira", Italy
Int School Dhaka, Bangladesh
NEMiles Jewish DS, AL
Madison MS, NM
Northwest MS, TN
NYC iSchool, NY
Waples Mill ES, VA
Swan River Montessori Charter School, MN




Background:

Eratosthenes, a Greek geographer (about 276 to 194 B.C.), made a surprisingly accurate estimate of the earth's circumference. In the great library in Alexandria he read that a deep vertical well near Syene, in southern Egypt, was entirely lit up by the sun at noon once a year. Eratosthenes reasoned that at this time the sun must be directly overhead, with its rays shining directly into the well. In Alexandria, almost due north of Syene, he knew that the sun was not directly overhead at noon on the same day because a vertical object cast a shadow. Eratosthenes could now measure the circumference of the earth (sorry Columbus) by making two assumptions - that the earth is round and that the sun's rays are essentially parallel.

He set up a vertical post at Alexandria and measured the angle of its shadow when the well at Syene was completely sunlit. Eratosthenes knew from geometry that the size of the measured angle equaled the size of the angle at the earth's center between Syene and Alexandria. Knowing also that the arc of an angle this size was 1/50 of a circle, and that the distance between Syene and Alexandria was 5000 stadia, he multiplied 5000 by 50 to find the earth's circumference. His result, 250,000 stadia (about 46,250 km), is quite close to modern measurements. Investigating the Earth, AGI, l970, Chapter 3, p. 66.

The formula Eratosthenes used is:

         D         A        d=distance between Syene and Alexandria
       _____  =  _____      A=360 degrees assumption of round earth
                            a=shadow angle of vertical stick
         d         a        D=to be determined (circumference)

How to Repeat the Eratosthenes Experiment Locally:

All you need to do is place a vertical stick (shaft) into the ground at your school and when the sun reaches its highest vertical ascent for the day (solar noon therefore the shadow length will be the shortest), measure the angle of the shadow of the stick (a).

                                -\
                                - \
                      stick ->  -  \
                                - a \    a=shadow angle
                                -    \
                                -     \
       ground___________________-______\shadow_______________________
Photographs of a student performing the the experiment.

Tip: Two ways to make sure the stick is in a true vertical position:

  1. Use a carpenter's level
  2. Use a rock tied to a string and dangle the rock above the ground in front of the stick
Tip: Determining solar noon for your location and time zone: By doing this experiment on the equinox we all know that the vertical rays of the sun are directly over the equator, like the well at Syene. Using a globe or an atlas, the distance between your location and the equator (d in equation) can be determined and the circumference can be calculated.
Share your results via the WWW with others around the real globe
  1. Between March 1-22, complete this on-line registration form with the following information:
  2.         Experimenter's/School's name:
            Location:
            Email address:
            School WWW address (if you have one):
            Anything else you might want to share: e.g., grade-level
  3. Between March 19- 21 perform the experiment

  4. (Note: Equinox is Tuesdayday March 20, 2012 )
  5. Between March 19-30, complete this on-line experiment report form with the following information:
  6.         Experimenter's/School's name:
            Location:
            Email-address:
            Latitude/longitude:
            Distance to the Equator:
            Measured shadow angle in degrees:
            Calculated Earth circumference:
  7. View the experimental results of others.
  8. Try answering one or more of the Eratosthenes Experiment Bonus Questions.
Tip: If you don't know your latitude and longitude, check the Geography server at http://www.mit.edu:8001/geo. Or, you can try the newer Rutgers Geography Server: telnet geogns.rutgers.edu 3000


Graphics scans of student work from St.Stephens School, Canterbury, Kent, UK.

James D. Meinke jmeinke@youth.net

Assist. Professor of Educational Technology
Baldwin-Wallace College, Berea, Ohio

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