Lafrançaise, France
March 2008
Flag | City | Country | School | Latitude (°) +N/-S | Longitude (°) +E/-W |
---|---|---|---|---|---|
Lafrançaise | France | Collège Antonin Perbosc | 44.127 | 1.238 |
Date | Gnomon | Shadow | Angle |
---|---|---|---|
September 17 | 100 cm | 90 cm | 41°59’ = 41.987° |
September 18 | 100 cm | 90.5 cm | 42°08’ = 42.145° |
September 19 | 100 cm | 90.5 cm | 42°08’ = 42.145° |
September 20 | 100 cm | 93 cm | 42°55’ = 42.923° |
September 21 | 100 cm | 94.5 cm | 43°22’ = 43.38° |
September 23 | 100 cm | 97 cm | 44°07’ = 44.128° |
September 24 | 100 cm | 98.5 cm | 44°34’ = 44.567° |
September 25 | 100 cm | 100 cm | 45°00’ = 45.000° |
September 28 | 100 cm | 104.5 cm | 46°15’ = 46.261° |
Lafrançaise (FR)
Latitude : 44°08’ N
Shadow :+90,0 cm —>N
Angle : + 42°00’
Home school, Stanford, Kentucky USA
Stanford (KY USA)
Latitude : 37°32’ N
Shadow :+ 72,0 cm—>N
Angle : + 35°45’
We had a good time participating in this project. Our weather has turned hot again, we would love some rain. The farmer’s crops and livestock really need it here.
695.75 km is the approximate distance between Stanford, KY and Lafrançaise, Fance.
The Circumference of the earth is 360 times the distance between cities divided by the central angle.
Circ. of earth = 360 X 694.41 / 6 = 41,745 km
Circumference equals approximately 41,745 km.
The actual circumference of the earth is 40,076 km.
September 17, 2007
Latitude difference : 44°08 ’- 37°32’ = 06°36’= 6.600 °
Distance : 6600 x 111.1 = 733 km
Angle difference: 42°00’-35°45’= 06°15’ = 6.250 °
Circumference: 733 x 360° / 6250° = 42221 km
++++Sept 18
Latitude : 44°08’ N
Shadow :+90.5 cm —>N
Angle : + 42°00’
++++Sept 19
Lafrançaise, Cañada de Gomez
Lafrançaise
Latitude : 44°08’ N
Shadow :+90.5 cm —>N
Angle : + 42°00’
Cañada de G.
Latitude : 32°49’ S
Shadow :+ cm —>S
Angle : - 34°40’
September 19, 2007
Latitude difference : 44°08 ’- (-32°49’) = 76°57’ = 76.950°
Distance : 76.950 x 111.1 = 8549km
Angle difference: 42°30’ -(-34°40’) = 77°10’ = 77.167°
Circumference: 8549 x 360 / 77.167° = 39 882km
New York
The Dwight School, 291 Central Park West,NY 10024
Latitude : 40°47’ N
Shadow :+ 82,0 cm—>N
Angle : + 39°20’
September 19, 2007
Latitude difference : 44°08’ - 40°47’ = 03°21’ = 3.350°
Distance : 3.350 x 111.1 = 372 km
Angle difference: 42°30’ - 39°20’ = 03°10’ = 3.167°
Circumference: 372 x 360 / 3.167 = 42 291 km
The school offers traditional athletics such as volleyball, basketball, baseball, soccer and tennis as well as academic teams such as the mock trials. We have many star parties throughout the year using our super telescopes in our roof top observatory.
I am scrambling to get our physics classes on the ball. This is our first time and we are not fully organized.
Sincerely,Kali
++++Sept 20
Lafrançaise
Lafrançaise (FR)
Latitude : 44°08’ N
Shadow :+93.0 cm —>N
Angle : + 43°00’
Wharton, New Jersey USA
Wharton, New Jersey USA
Latitude : 40°54’ N
Shadow :+84,0 cm—>N
Angle : +40°00’
September 20, 2007
Latitude difference : 44°08’ - 40°54’ = 03°14’ = 3,233°
Distance : 3,233 x 111,1 = 359 km
Angle difference: 43°00’ - 40°00’ = 03°00’ = 3,500°
Circumference: 359 x 360° / 3,000° = 43 080 km
6A writes…….Our class is in the Alfred C. MacKinnon Middle School. We have great teachers and it’s a small middle school .We have a dress code at MacKinnon Middle School. Most of the students wear casual clothing like jeans and t-shirts, but we cannot wear flip-flops, tank shirts or shirts with inappropriate sayings on them. We also have school sports like baseball, soccer, cross country, softball and cheerleading.
6B writes……. Our class is in the Alfred C. MacKinnon Middle School in Wharton, New Jersey. It is a great school with great teachers and we have baseball, softball, soccer, basketball, cheerleading, and cross country teams. We also have clubs after school like art, homework, and computer club. We have a great principal and a great cafeteria. As 6th graders, this is first time changing classes for every subject. In 8th grade we will get to go to Boston, Massachusetts over night and get to learn about the History of Boston!
6C writes…….Good Day! We are 6C and we are participating in the Noon Day project as part of a school wide enrichment program. Our school is MacKinnon Middle School. It is located in Wharton, NJ. MacKinnon Middle School has a lot to offer. We have great teacher for all of our classes. They work hard to help us do our best. We have a great sports program that includes soccer, basketball, baseball, cheering, and cross-country. Our performing arts department includes chorus, drama and band. Here in Wharton, we also get the opportunity to attend community events such as dances and carnivals. Our community works hard to give each resident the feeling of family.
6D writes…….I am writing this letter on behalf of my 6D class. My name in Andrea Guaman. I live in Wharton NJ. I go to school here in MacKinnon Middle School. I am 12 years old. I’m from Ecuador. I’m in the 6th grade . The name of my homeroom teacher is mrs Winkler. This is my first year here in MacKinnon Middle School.
MacKinnon Middle School
Wharton, NJ 07869
6th Grade Math and Science
Teachers: Mrs. Riordan, Mrs. Silvestri, Mrs. Kepler, Mrs. Allen and Mrs. Leary
Activities:
As a part of our district’s schoolwide enrichment program 6th graders were introduced to the Noo Day Project via a series of lessons and activities conducted by our technology teacher, Mrs. Leary. Some of the lessons included online movie segments, use of Geometer’s Sketchpad, hands on models and simulated practice sessions for the big event.
Once the students were well prepared for the actual measurements the entire Class of 2010 met in our front parking lot to record angle measures of the sun. Our recordings took place on September 20th. We were fortunate to have been granted a beautiful, sunny day. The students set up their measuring stations which they had constructed from cans of sand, meter sticks, protractors, string and plumb lines. Our recordings were made on roll paper. Checks for accuracy were done back in the classrooms.
During the following week students selected Gulf Breeze, Florida as their partner and proceeded to calculate the circumference of the earth. As a reminder of the steps in this mathematical process we used a song composed by previous MacKinnon students. It is entitled "Old Eratosthenes Had a Way" and can be accessed via a PowerPoint slideshow on our school’s math website. You can view this show @ http://mcubed4.tripod.com/id8.html .
Students used their tech class time to write essays on their Noon Day experience. These were share in their math and science classes. The overwhelming response to this project was very positive. Students enjoyed the cross curicular nature of the event, the hands on learning and the use of technology infusion. With this in mind, the district is considering repeating the project with grade seven in the spring.
Final results:
The four sixth grade classes calculated the earth’s circumference to be about 41,652 km. To obtain this result each of the small groups within each class submitted their group calculations for a class discussion on measures of central tendency, outliers, and other elements of the the experimental process. A class vote was taken to determine the "best" answer. Many of the students also "discovered" the relationship between the measured angle and their latitude. Overall, the experience was a very positive one.
++++Sept 21
Lafrançaise
Lafrançaise (FR)
Latitude : 44°08’ N
Shadow :+94,5 cm —>N
Angle : + 43°20’
Yuba City, California, USA
Latitude : 39°06’ N
Shadow :+78,45cm—>N
Angle : + 38°10’
September 21, 2007
Latitude difference : 44°08’ -39°06’ = 05°02’ = 5,033°
Distance : 5,033 x 111,1 = 559 km
Angle difference: 43°20’ -(-38°06’) = 05°14’ = 5,233°
Circumference: 559 x 360° / 5,233° = 38 454 km
We are the first 6th grade class at a brand new school in Yuba City, California, USA, called Riverbend Middle School.
We are located in a farming community north of Sacramento.
We are a math and science exploration class, which is an elective class offered for strong math students.
Throughout the year we will be studying both math and science through hands-on projects.
Our latitude is 39°05’15" N.
Our longitude is 121°36’04"W.
Thank you to all the classrooms sharing the wonder of new things with us!
Adélaïde, Australie
Adélaïde
Latitude : 35°00’ S
Shadow :+70,0 cm—>S
Angle : - 35°00’
Hamilton Secondary college is a large secondary government school with both continuing students from grades 7-12 and also adult students who attend day and night classes in a variety of curriculum areas. We are situated in the southern suburbs of Adelaide around 6 km from the sea and 7 km from the CBD. Hamilton is the home of the South Australian Space School and we frequently have NASA astronauts visit our school.
Students play a variety of sports including basketball, volleyball, netball,cricket, Aussie rules football, soccer and we also have a large number of students involved in rock climbing (we have a rock wall on site) and bike riding.
The Australian Rules Grand Final is to be played this week in Melbourne and the two teams playing are Geelong ( a town near Melbourne) and a team from Adelaide (Port Adelaide ’Power’). Over 40,000 people are expected to travel to Melbourne from Adelaide to watch the teams play.
We have a mediterranian climate here with temperatures ranging from 8-12 degrees C max in winter to 33-40 degrees C maximum in summer. At the moment we are in spring with temperatures around the mid twenties. There is 16.5 hours time difference between Adelaide and LA (on daylight saving) so that when it is 6pm on Sunday 23 September in LA it is 10.30 am in Adelaide.
September 21, 2007
Latitude difference : 44°08’ -(-35°00’) = 79°08’ = 79,133°
Distance : 79,133 x 111,1 = 8791 km
Angle difference: 43°20’ -(-35°) = 78°20’ = 78,333°
Circumference: 8791 x 360° / 78,333° = 40 401 km
Warren, Oregon,USA
Mrs. Rosenthal’s 3rd grade advance math students took on the challenge of the noon day project. In Oregon the sun comes out for brief parts of the year and primarily in the summer. We are known for our liquid sunshine. My name is Catherine Hay, a parent volunteer whose love for math gave me the opportunity to work with this group.
On our best day for sun, the students learned the basic principles of measurements with a meter stick, and how to read one.
The next step was to understand the definition of perpendicular verses parallel. This was used when we constructed our shadow measurement tool. Parallel and perpendicular with the ground were used in our math vocabulary. We grouped into two teams, which measured and recorded data. This data was then brought back to the classroom and a comparison was done. These third graders then learned about approximation and how to analyze the data. From the data they watched the measurements decrease and were able to see that as the sun gets higher in the sky the shadow measurements got smaller. They also saw the data collected by the teams were different but were still decreasing. Base on the team’s measurements they then used their skills to produce a best approximation. Rounding was used to produce the measurement of 91.5 cm.
We then talked about what a protractor looks like and what it does. We related our findings to skateboarding. A 360 is a full circle, and a 180 is only a half of a circle. We also discussed that it is measuring degrees of an angle. We then constructed a right angle with two 100 cm sticks, which we say were perpendicular to each other to form the right angle 90 degrees. We marked our 91.5 on one stick and took a straight edge of butcher paper, from that point to the top of the other meter stick. We then measured the angle it created at the top our triangle. They came up with 45 degrees.
We then drew circles. 360 degrees. They used a protractor to mark off every 45 degree in a 360, coming up with 8.
Because these are third graders, we used the program on the noonday site to measure the distance from our school to the equator. Our information resulted in 5075 km. They are just starting to understand their times table, so we worked on multiplying 5075 * 8 resulting in 40600 km. Not bad, considering they are learning. This then was related to the circumference around the earth, and we pulled out our globe to take another look.
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We then were given our partner school. This resulted in the group learning where Wharton, New Jersey is located. Because the schools are not North/South of each other, we used the program to calculate the distance from the equator for both schools.
Warren= 5075km; Wharton=4518km
We then subtracted them from one another to get 557km between them.
This then was used with the process of subtracting the schools angles. Warren at 45 degrees – 40 degrees of Wharton, to get 5 degrees. We then needed to find how many 5 degrees are in a 360. We got 72.
From this we then calculated 72 * 557= 40104 km as the circumference of the earth.
Our group had a ton of fun and the experience gave them great pride that they were completing a project along with older math students. Many math concepts were taught in a fun learning environment. We may be little but we are math strong.
Chillicothe, Ohio , USA
Greetings from Chillicothe, Ohio! Our 12th grade physics class divided into groups and gathered our data on September 21, 2007. Local noon was at 1:23 pm, so a team of students met at 1:05 pm and started to take measurements at 1:11 pm. We used rectangular meter sticks taped to bricks. We checked with a level to be sure the meter sticks were perpendicular. We had poster boards taped together under the meter sticks. We marked the edge of the meter stick, then the shadow’s edge every two minutes until 1:41 pm. Here are some pictures of the Measuring Team at work.
When our measurements were complete, the rest of the student teams went to work. They measured the length of each shadow line to find the shortest one, then they used trigonometry to find the sun angle measure. To do this, they found the ratio of the shortest shadow’s length in cm divided by the meter stick’s length of 100 m, then used inverse tangent (tan-1) to find the angle measure. Most of our angles were near 38 degrees.
The next step was to choose a school in the Southern Hemisphere and combine our data with theirs. Their angle and our angle were added to find how large of a slice of the earth’s total angle measure from N to S we had combined. For instance, if their angle was 32 and ours was 38, we had a total of 70 degrees combined. By multiplying this angle measure by 111 kilometers per degree, we found the N – S distance between our locations.
Then we took 360 divided by 70 degrees to find the number of “slices” of this size in the whole earth. Finally, we multiplied the number of slices times the number of kilometers per slice to find the earth’s circumference. All of our teams were under 5% error. Until next year – this is Unioto High School, over and out!!
++++Sept 23
Lafrançaise
Photo by Laure (5 ° 1) at her home on Sunday, for the autumnal equinox.
Auckland , New Zealand
We are a home school family in Auckland New Zealand. We are Year 6 which is equivalent to Grade 6 USA. We are starting this experiment with great pleasure. We are looking forward to do the activities and the noon day itself. Our location is: Latitude: 36°52’03" South Longitude: 174°48’12" East We found this on Google Earth. We are in Spring time here down under with the sun shining most days. Let’s hope it’s sunny on the DAY!
Pachuca, México
lat: 20°07’ N long: 99°44’ W
Greenfield Park (CANADA)
St. Jude School : Final Report
Our school is located in a suburb of Montreal, Canada, at 45:29N (latitude) and 73:29W (longitude). We are 28 students in grade 5(class5IA). Our teacher, Mrs. Mirza introduced this project to us in September. She explained to us how Eratosthenes performed a simple experiment 2200 years ago to measure the circumference of the Earth. His calculation is still considered accurate today by scientists.
We went on the Noonday website and did some research. At first, the whole idea appeared quite complicated to us. Most of us had trouble understanding some ideas and how they were going to help us determine the circumference of the Earth. But as we got more involved, the process started to become clear.
We carried out the shadow measurements on September 21 st 2007, which was as close as we could get to the Autumn Equinox (September 23 rd). The shadow measurements (99cm) at high local noon time (12:48pm) helped us determine our sun angle which was 44 degrees.
The next step was to choose a partner city whose sun angle could help us find the central angle. We decided to select Abba’s Orchard in Philippines, as it is far away. Their sun angle was 8.4 degrees. The difference between the two became our central angle, that is, 35.6 degrees.
Now Mrs. Mirza showed us how the central angle could be compared to a slice in a big circle. We could then understand that the arc of the central angle represented the distance between the two cities. Once we knew the North/South distance between us and Abba’s Orchard, by subtracting the 2 latitudes, we could then multiply the arc’s length with the number of slices in a circle. These are some of our calculations:
No. of slices= 360°divided by 35.6 degrees=10.1
N/S distance= 4 116.25 km
Circumference of the Earth = 4116.25x 10.1 = 41, 574.12 km
Conclusions : We learned a great deal from this project. We now know how knowledge of angles helps us in real life, how the circumference is calculated and much more. Before doing this project we didn’t know a lot about latitude and longitude and what these lines help us find on the globe.
All of us are very proud of our learning. We can see how Math, Science and Technology work together in any scientific study.
Students of Class 5IA
++++Sept 24
Lafrançaise
Latitude | Ombre/Shadow | Angle | |
44°08’ N | Lafrançaise (FR) | +98,5 cm —>N | + 44°30’ |
08°25’ N | Baungon (Philippines) | +15,25 cm—>N | + 08°40’ |
Baungon, Philippines : The Abba’s Orchard.
Our students are just wrapping up their parent-teacher-student conferences this week and should be getting on the noonday project shortly. Our school’s exact bearings read:
8° 25’ 8.55’’ North, 124° 38’ 4.65’’ East.
Arras, école Lafontaine
Latitude | Ombre/Shadow | Angle | |
44°08’ N | Lafrançaise (FR) | +98,5 cm —>N | + 44°30’ |
50°17’ N | Arras (FR) | +123,0 cm—>N | + 51°00’ |
The day after the equinox, in spite of bad weather conditions, we were able to do a few measurements. The value of the angle of the sun’s rays with the vertical (51 °) is close to the value of Arras latitude (50 ° 17 ’).
Maricopa, Arizona, USA
Latitude | Ombre/Shadow | Angle | |
44°08’ N | Lafrançaise (FR) | +98,5 cm —>N | + 44°30’ |
33°03’ N | Maricopa (Arizona USA) | +64,00 cm—>N | + 34°00’ |
We are an 8th grade Pre-Algebra class at Maricopa Wells Middle School in Maricopa, Arizona, U.S.A.
We are located Latitude (33) Longitude (-112).
Our city and school is in a great growth at this time. A couple years ago our middle school had 300 kids; now we has 1270 and still more are coming! We have a dress code of simple designs/plain shirts and pants, and we have a great sports program with football, volleyball, soccer, basketball, cheer, and cross country. We have a great staff and student population and we are getting excited for this well put together project...goooo Eratosthenes!!
Mrs. Gomez’ 8th Grade, 5th Hour Pre-Algebra Class
When I caught up with the class on Wednesday, September 26th, they had already been working with several days worth of sun movement measurements.When I met up with them outside their classroom, at the start of 5th hour, students were already aligning and stabilizing meter sticks that would be used as one of their tools. Underneath the sticks, they had first set down butcher paper. The stick cast the sun’s shadow on the paper and the small teams were directed by the teacher to take new measurements every 2 minutes for 10 minutes. This was the data collection phase.
Along with this and several other days of data the students are developing mathematical and statistical ways to analyze and interpret their data - to make it meaningful. The collaborative portion of this project derives from the publishing and evaluation of many class findings. The students in Mrs. Gomez’s class were viewing data submitted by students in other countries, far flung geographic locations, who are conducting the same project NOW!
Students will now work to calculate the circumference of the Earth, prepared with a good understanding of mathematics, the measurements of their simple tools and methods, and factoring in data published from a worldwide host of contributors ! They viewed data and pictures from Australia, Philippines, France and more!
Gulf Breeze, Florida USA
Latitude | Ombre/Shadow | Angle | |
44°08’ N | Lafrançaise (FR) | +98,5 cm —>N | + 44°30’ |
30°22’ N | Gulf Breeze (FL USA) | +56,0 cm—>N | + 30°00’ |
Hello from Oriole Beach Elementary! We’re located at 30.17 N latitude and 87.10 W longitude...just a few miles east of Gulf Breeze, Florida. We’re not on a beach but Pensacola Beach is only a 10 minute drive away. We have 850 Pre-K to 5th grade students in our school. Two of the six 5th grade classes are participating in this project. Our teachers team up for our math and science.
Virginia Beach, USA
Latitude | Ombre/Shadow | Angle | |
44°08’ N | Lafrançaise (FR) | +98,5 cm —>N | + 44°30’ |
36°45’ N | Virginia Beach(VA USA) | ....... cm —>N | + 37°11’ |
Our average measurement of the shadow was 9.2 inches from a foot long stick 12.125 inches.
This gave us a central angle of 37.18 degrees.
Our distance to the equator is 2528 miles.
Therefore using the proportion, we measured 24,478 miles.
The actual circumference is 24,902 miles.
Our percent error was -1.7%.
++++Sept 25
Lafrançaise
New York, Brooklyn, USA
Greetings from Brooklyn Friends School! We are located in Brooklyn, New York in the U.S. Our Latitude is 40.41.36 N and our longitude is 73.59.17 W. We are a Quaker school and we have around 600 students from family center to 12th grade. We have around 130 faculty members. New York is home to many important buildings and structures like the Empire State building and the Statue of Liberty. And we are not far from ground zero; where the World Trade Center used to be.
Middle Schoolers Perform the World’s Greatest Experiment
by Jeffrey Stanley
Janet Villas’ eighth grade Earth Science class is studying the dimensions and movement of the Earth right now, so the special “Noon Day” project undertaken by kids around the world fit in perfectly with her lesson plans.
“Our measurement at Clearpool was a one second reading with the sun darting in and out of clouds,” she said, “so we used our Brooklyn backup measurement instead. Our students did a great job and had to take it home and try to do the calculations themselves.”
The measurement in question, using the sun to determine the Earth’s circumference, was part math, part science, part historical reenactment.
“Eratosthenes was the librarian at the Great Library in Alexandria, Egypt,” explained Janet. “He devised a way using simple shadows to calculate the circumference of the Earth with astonishing accuracy about 2300 years ago.”
In what the New York Times once called the number one experiment of all-time, Eratosthenes did pretty much this: he looked up at the noon day sun directly overhead in a town he was visiting, and he knew that at noon back in his hometown of Alexandria the sun was 1/50th of a full circle away from directly overhead at the same time of day. He put two and two together and figured that the geographic distance between the two towns must therefore equal 1/50th of the Earth’s circumference, so he calculated the distance between the two towns and multiplied by 50. His result, about 25,200 miles, was pretty accurate (the Earth’s average circumference is 24,860 miles or 40,008 km).
Janet’s students reenacted Eratosthenes’ discovery by participating in the Noon Day Project, an international event which can only happen twice a year at the equinoxes.
Created by Stevens Institute of Technology in Hoboken, the project links schools and students together to share data and calculate the Earth’s circumference together. “Students can easily recreate this experiment, but they need to partner with another school somewhere far away to get results,” Janet explained.
“We had to construct a gnomen, or large sundial, to cast a shadow, then read the shadow at precisely noon and calculate the angle and length of the shadow.” They took the main reading during the eighth grade’s leadership retreat at Clearpool Education Center in Carmel, New York on September 27th but the uncertainty caused by cloud cover made them opt to go with a previous in-class reading instead.
They then picked Miami Dade County School’s data from the Noon Day Project’s website because they’re in the same hemisphere as BFS and gathered their data on nearly the same day. “Our answer was 39, 960 km which is darned close to the actual answer of 40,008.”
One might question the necessity or value of determining the circumference of the Earth when students can easily look it up in a textbook but Janet sees it differently. “The real excitement is that it’s possible to find out such a big thing on your own with a simple shadow stick." She also stressed the communal value of the Noon Day Project. “It’s exciting to think that others just like you are also pondering this experiment. It proved that the Earth must indeed be a sphere.”
Wrocław, Pologne
Liceum Ogólnokształcące : 51,11°N 17,11° E
++++Sept 28
Lafrançaise
Naples, Florida, USA
Our school is a public A-rated school. There are 24 kids in this class, and 770 kids in the school. We have an outstanding challenge program and wonderful teachers of every type, even for art! Pelican Marsh has a morning News program that all of the teachers tune their TVs to the channel, and the volunteers from the 5th grade make announcements on. The 5th graders also make a security system that we like to call the Safety Patrols. The kids help the littler one to their classes and open the car doors in the car line. There are some cool fun-facts about Pelican Marsh!
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