Measuring the radius of the Earth – Eratosthenes 2023 experiment
The Panhellenic school activity of calculating the radius of the Earth according to the method of Eratosthenes stands out in our school activities in recent years.
With the mission of the latest school unit praise and teacher certifications also complete, as a reflection, it is worth dwelling on the specifics of a collaborative, multi-thematic and multi-beneficiary effort, adaptable to the levels of instruction and educational requirements of today and tomorrow.
This year’s event, on the day of the vernal equinox, Monday, March 20, 2023, was also very successful.
At the time of the meridian of the Sun, about 20,000 enthusiastic students under the guidance of their 2,000 teachers in 600 primary and secondary teaching units, they measured the lengths of the rods and their shadows and, with calculations adapted to each level of education, managed to calculate the length of the circumference and the radius of the Earth, with an error of 0.38%! The distribution of participating structures is represented schematically as follows:
The action was organized by the Panhellenic Union of Natural Science Laboratory Center Managers (PAN.EKF.E.), with the approval of the Ministry of Health (prot. no. 26911/GD4/09-03 -2023) and the support of the Institute of Astronomy, Astrophysics, Space Applications and Remote Sensing (IAADET) of the National Observatory of Athens and was coordinated by a group of fifteen members of the heads of the centers laboratory for natural sciences (EKFE). It is a continuation of the one organized during the 2018-2019 school year (accreditation 158982/Δ7/25-09-2018), by EKFE Serres, Pieria, Laconia, Thesprotia, Kos and Argolis.
Highlighting experimentation as an integral component of the educational process and engaging students and teachers in experiential and collaborative discovery activities is the primary goal and objective. Moreover, the interdisciplinary combination of knowledge and practices from the natural sciences, technology, mathematics, engineering, computer science, etc. combined with the enthusiastic active participation of students and teachers, gives popular educational activity remarkable dimensions, educational, pedagogical, but also cultural!
Building on the experience of previous years, out of respect for the passion of worthy colleagues and for reasons of organization, security and functionality, the action has developed this year in a new digital space “moodle”. This area hosts the rich educational material with instructions – tips for performing the measurement, worksheets, presentations, videos, etc. At the same time, this original community of teachers who are keen to equip their students with knowledge using imaginative and innovative methods such as the internationally renowned “Eratosthenes’ experiment” is developing here in cooperation. The pilot application of the community in “moodle” was considered successful by common consent, contributing to the strengthening of cooperation, communication, teamwork, direct mutual aid and easy exchange educational digital material. The community -quantitatively and qualitatively strong- thus created becomes the basis for the future development of the multidimensional action of Eratosthenes, but also of many others, since it proves in practice both the dimension of the feasible, of the pleasant, functional and remarkably efficient. project.
The students and teachers who participated in this versatile activity deserve congratulations because they leave no doubt that perseverance and passion are the guarantee of a better future!
Description of the educational activity
Although the historic experience took place on the day of the summer solstice (June 21), for convenience it is repeated by the school community on the spring equinox. Thanks to the valuable advice of their teachers, students of all ages, without moving or traveling, simply following in the footsteps of the scientist Eratosthenes, have managed to calculate the circumference and the radius of the Earth with satisfactory precision! The experiment was carried out throughout the week of March 20 to March 24, 2023 by school units that the weather conditions did not allow them to measure on March 20. In this case, an appropriate correction of the result was carried out. The statistical processing of the measurements gave the following impressive diagram:
Eratosthenes with unique resources of intellect, knowledge, curiosity, scholarship and the poor means of his time, achieved the impossible. In the modern era, student supplies include a variety of tools from digital technologies. Appropriate software was used to calculate geographical coordinates, distance from a place to the equator or the appropriate time of the experiment such as Google Maps application, Google Earth software, SunCalc program, web applications as well as mobile phone applications. Following modern educational trends, this year’s action has been enriched with innovative digital tools using mobile devices (tablets and mobile phones). In addition, groups of students from schools in different regions of Greece had the experience of participating in an original online knowledge game and competing with other groups on topics related to Eratosthenes and his historical experience. , learning in a fun and playful way. Thus, the collective nature of the experimentation has been highlighted, the students’ interest has been stimulated with tools that are familiar to them and alternative ways of carrying out a common educational activity have been applied to a very diverse public in terms of of knowledge and skills.
The image captured in the schoolyards through the photographic material collected revealed the ingenuity, dexterity and passion of the pupils and teachers who fixed rods or other everyday objects, measured their lengths, the lengths of their shadows and calculated angles. The so-called “geometers”, despite the lack of intense sunshine in certain regions, took advantage of the slightest radius of the Sun and were led to calculate the radius of the Earth with remarkable precision and an error of less than 0.38% in many many cases!
The “added value” of Eratosthenes’ experience
By performing this historical experiment, students will:
● participate with interest in a lesson rich in knowledge and lessons, not only in class, but also in the courtyard of their school,
● they learn through experience that with simple measurements of physical quantities, with observations, hypotheses, appropriate reasoning and above all with their will, they can be led to measure the very circumference of a star like the Earth,
● discover processes, observe phenomena and understand concepts (measurements, precision, errors), become familiar with the terminology of Geography and Astronomy (eg coordinates, solstices, equinoxes, etc.) but also appreciate historical continuity science,
● they are taught in the most demonstrative way the unshakeable power of documented scientific knowledge and the timeless and unsurpassable contribution of the Positive Sciences to the understanding of the universe,
● they realize the inestimable value of cooperation, since in this activity they cooperate in an exemplary, fruitful and creative way:
– the pupils, when taking measures and decisions in each school class,
– teachers, from schools located in remote areas, who exchange their measurement data and carry out joint calculations,
– important and functional educational structures, such as the EKFE
A few words about the history of the experiment
Eratosthenes (3rd century BC) was director of the great Library of Alexandria, where he read in a papyrus that at noon on June 21 (summer solstice), in Syene (Aswan), the pillars verticals cast no shadows and the Sun was reflected at the bottom of a well. But he noticed that in Alexandria, on the same day, the vertical pillars cast a shadow. He reasoned that if the Earth were flat, the vertical poles of the two cities would be parallel and both should cast shadows. So, since it’s not true, what could be happening? The answer was given by Eratosthenes, arguing that the Earth’s surface is not flat, as was thought at the time, but spherical. The calculation of the radius of the Earth can be done if one knows the distance between Syene and Alexandria – which, according to testimony, Eratosthenes hired “leaders” to measure – and the difference in latitudes of the two cities, which has been calculated (from the length of the shadow of an obelisk) approximately equal to 7 degrees.
Eratosthenes calculated the circumference of the Earth at 39,375 km, using as his only tools sticks, eyes, feet, mind with simplicity of thought and ingenuity. The error in the calculation was only 2%, a truly remarkable achievement for 3rd century BC data. Therefore, Eratosthenes was the first person to measure the dimensions of the planet Earth, which is why he is considered the creator of mathematical geography.
- Georgopoulos Christos, President of PAN.EKFE, Director of EKFE St. Anargyron,
- Gatsis Aristidis, Director of EKFE Karditsa,
- Anastasia Gigoudis, director of EKFE Toumbas (An. Thess/nikis),
- Irini Dermitzaki, leader of the 2nd EKFE Heraklion,
- Maria Theologu, Director of EKFE Polygyrou (Chalkidiki),
- Sophia Kyriazopoulou, Director of EKFE Rhodopes,
- Lazos Panagiotis, Director of EKFE Iliopolis,
- Manousaki Cleopatra, head of EKFE Argolida,
- Michou Despina, director of EKFE Grévenon,
- Pazoulis Panagiotis, director of EKFE drama,
- Eleni Paloumba, Director of EKFE Laconia,
- Eleftheria Papadeli, Director of EKFE Kozanis,
- Anna Sotiropoulou, Director of EKFE Messinia,
- Konstantinos Chalkiadakis, Director of EKFE Rethymnon,
- Nikolaos Charalambakis, Director of EKFE Ilias
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