Οι τυροκόμοι ... της Β τάξης

Το δικό τους τυρί παρασκεύασαν οι μαθητές της Β τάξης με τη βοήθεια της γιαγιάς του συμμαθητή τους Κωνσταντίνου Περδίου. Η γιαγιά Γιάννα έφερε φρέσκο γάλα από τα πρόβατα που συντηρούν και βήμα - βήμα τους έμαθε πως φτιάχνεται το τυρί φέτα. Στο γάλα που βράστηκε κι έφτασε στην κατάλληλη θερμοκρασία που τη διαπίστωσε με εμπειρικό τρόπο, πρόσθεσε τη διαλυμένη σε νερό πυτιά και αφού ανακάτεψε καλά για λίγη ώρα το άφησε να ξεκουραστεί τυλιγμένο για μία ώρα. Μετά πήρε το σκεύος με το γάλα που είχε πια αρχίσει να στερεοποιείται κι αφού το χάραξε σε κομμάτια το άδειασε στην τσαντίλα όπου το πίεσε για να φύγει το το τυρόγαλο. Η τσαντίλα κρεμάστηκε για να στραγγίξει  τελείως. Το τυρί θα αφαιρεθεί από την τσαντίλα μετά από μία μέρα και θα είναι έτοιμο μετά από ένα τρίμηνο αφού θα ωριμάσει τοποθετημένο σε άλμη. Στην επόμενη συνάντηση η γιαγιά Γιάννα θα μας μάθει τα μυστικά παρασκευής του κασεριού κι άλλων ειδών τυριού που παρασκευάζονται στο τόπο μας. 

The cheese makers ... the second grade

Theirs cheese preparations students of the class with the help of his grandmother classmate Constantine Perdiou. Grandmother Gianna brought fresh milk from sheep that maintain and step - step taught them that feta cheese is made. The milk was boiled and reached the appropriate temperature establishing it empirically, added the rennet dissolved in water and after toss well for a while let it rest wrapped for one hour. After he took the pan with the milk had already begun to solidify and after the engraving pieces emptied in vexation where pressured to leave the whey. The vexation hung to drain completely. The cheese is removed from the vexation after one day and will be ready after a quarter after it matured placed in brine. At the next meeting Gianna grandmother would teach us the secrets of Caserta manufacturing and other types of cheese manufactured in our country.

Marrësit djathë ... klasën e dytë

Tyrja përgatitjet djathë nxënësit e klasës me ndihmën e klasës së tij gjyshes Constantine Perdiou. Gjyshja Gianna solli qumësht të freskët nga delet që ruajtur dhe hap - hap i mësonte ata se djathi feta është bërë. Qumështi u zier dhe të arritur temperaturën e duhur për themelimin atë empirike, shtoi mullëz tretur në ujë dhe më pas hedh edhe për një kohë le të pushoni përfundoi për një orë. Pasi ai mori pan me qumësht kishte filluar tashmë të ngrij dhe pas copa gdhendje zbrazur në shqetësimin ku presion të largohen nga hirrë. Shqetësimin varur të thahet plotësisht. Djathi është larguar nga shqetësimin pas një ditë dhe do të jetë gati pas një çerek pasi pjekur vendoset në shëllirë. Në takimin e ardhshëm Gianna gjyshja do të na mësojë sekretet e prodhimit Caserta dhe llojet e tjera të djathë të prodhuara në vendin tonë.

 

Η χορωδία του Σχολείου μας ... στην εκδήλωση των ειδικών σχολείων

Η χορωδία του Σχολείου μας θα συμμετάσχει στην γιορτή λήξης του Ειδικού Δημοτικού Σχολείου και Ειδικού Νηπιαγωγείου Αγριάς την Τρίτη 2 Ιουνίου 2015, 7:30 μ.μ. στο Πολιτιστικό Κέντρο της Νέας Ιωνίας Βόλου. Ήδη η χορωδία συμμετέχει τις συναντήσεις προετοιμασίας της εκδήλωσης μαζί με τους μαθητές των σχολείων που συμπράττουν στην εκδήλωση στο Πολιτιστικό Κέντρο της Νέας Ιωνίας Βόλου. 

The chorus of our school will participate in the closing celebration of the Special Primary School and Special Kindergarten Agria Tuesday, June 2, 2015, 7:30 pm at the Cultural Center of Nea Ionia Volos. Already the choir participates on the event preparation meetings with the students of schools that collaborate to the event at the Cultural Center of Nea Ionia Volos.

Kor i shkollës sonë do të marrë pjesë në festimin e mbylljes së Shkollës Fillore Speciale dhe Kopshti i fëmijëve Speciale Agria e martë, qershor 2, 2015, 19:30 në Qendrën Kulturore të Nea Ionia Volos. Tashmë kori merr pjesë në takimet përgatitore ngjarje me nxënësit e shkollave të cilat bashkëpunojnë për ngjarje në Qendrën Kulturore të Nea Ionia Volos.

Σχετικά με τις εγγραφές μαθητών

Σας ενημερώνουμε για τα απαραίτητα δικαιολογητικά εγγραφής στην Α τάξη του Δημοτικού Σχολείου. Για οποιαδήποτε διευκρίνιση επικοινωνείτε με το γραφείο του Σχολείου  (τηλ. 2428090240)

We inform you about the necessary registration documents to the first grade of primary school. For any clarification please contact the school office (tel. 2428090240)

Ne t'ju informojë në lidhje me dokumentet e nevojshme për regjistrim në klasën e parë të shkollës fillore. Për çdo sqarim ju lutem kontaktoni zyrën e shkollës (tel. 2428090240)

Κάθε στίχος μία ιστορία ... η παράσταση!

Με μια ονειρική παράσταση ολοκληρώθηκε το καινοτόμο πρόγραμμα "Κάθε στίχος, μία ιστορία ..." που υλοποιήθηκε από τα σχολεία 1ο Δημοτικό Σχολείο Πορταριάς "Ν. Τσοποτός", 13ο Δημοτικό Σχολείο Βόλου και 2ο Δημοτικό Σχολείο Αρτέμιδας - Κάτω Λεχωνίων "Τοπάλειο".

Στο κατάμεστο κινηματοθέατρο "Αχίλλειο" οι μαθητές που συμμετείχαν μας ταξίδεψαν στο μελοποιημένο έργο των Σεφέρη, Ελύτη και Γκάτσου μέσα από τα τραγούδια, τις αφηγήσεις, τις δραματοποιήσεις που δημιουργήθηκαν με την εμψύχωση των δώδεκα συνολικά εκπαιδευτικών που συμμετείχαν στο πρόγραμμα. 

Παράλληλα πραγματοποιήθηκε και συλλογή τροφίμων για το Κοινωνικό Παντοπωλείο του Δήμου Βόλου με τη βοήθεια της ομάδας διασωστών, ενισχύοντας έτσι το κοινωνικό έργο που επιτελείται για την ανακούφιση συμπολιτών μας.

Το πρόγραμμα θα κλείσει με την παράδοση του ψηφιακού βιβλίου και των αντίστοιχων αφηγήσεων στους μ,μαθητές που συμμετείχαν στη λήξη της σχολικής χρονιάς.

Κάθε στίχος μια ιστορία ...

Θα πραγματοποιηθεί τη Τετάρτη 13 Μαΐου 2015 στις 6 μ.μ. στο κινηματοθέατρο "Αχίλλειο" κοινή εκδήλωση των σχολείων 1ο Δημοτικό Σχολείο Πορταριάς "Ν. Τσοποτός", 13ο Δημοτικό Σχολείο Βόλου και 2ου Δημοτικού Σχολείου Αρτέμιδας - Κάτω Λεχωνίων "Τοπάλειο" για την ολοκλήρωση του καινοτόμου προγράμματος που υλοποιήθηκε τη σχολική χρονιά 2014 - 2015 με τίτλο "Κάθε στίχος, μία στίχος ...".

Η εκδήλωση έχει και κοινωνικό χαρακτήρα καθώς γίνεται έκκληση σε όσους παρευρεθούν, αν επιθυμούν, να συνεισφέρουν είδη για  την ενίσχυση του Κοινωνικού Παντοπωλείου του Δήμου Βόλου.

Στην εκδήλωση θα ακουστούν μελοποιημένοι στίχοι των  Γιώργου Σεφέρη, Οδυσσέα Ελύτη και Νίκου Γκάτσου που προσεγγίζονται από τους συμμετέχοντες μαθητές με τραγούδι, κίνηση και δραματοποίηση.

Will be held on Wednesday, May 13, 2015 at 6 pm in cinema "Achilles" common manifestation of schools 1st Primary School Portaria "N. Tsopotos" 13th Primary School of Volos and 2nd Primary School of Artemida - Lower Lehonia "Topaleio" to complete the innovative program that was implemented in the school year 2014-2015 with title "Every verse, one verse ...".
The event has a social character as it becomes appealing to those who attend, if they wish, contribute articles to strengthen the Social Grocery of the Municipality of Volos.
The event will be heard set to music lyrics of George Seferis, Odysseus Elytis and Nikos Gatsos accessed by the participating students with song, movement and drama.

Do të mbahet në e mërkurë, maj 13, 2015 në 06:00 në kinema "Akil" manifestim i zakonshëm i shkollave Shkolla Fillore 1 Portaria "N. Tsopotos" Shkolla fillore 13 e Volos dhe Shkolla e ARTEMIDA 2 Fillore - Lehonia Ulët "Topaleio" për të përfunduar programin inovative që u zbatua në vitin shkollor 2014-2015 me titull "Çdo ajet, një ajet ...".
Ngjarja ka një karakter shoqëror pasi të bëhet tërheqës për ata që marrin pjesë, në qoftë se ata dëshirojnë, të kontribuojnë artikuj për të forcuar ushqimore Sociale e Komunës së Volos.
Ngjarja do të dëgjohet të vendosur në tekst muzikë e George Seferis, Elitis Odiseut dhe Nikos Gatsos arrihen nga studentët pjesëmarrës me këngë, lëvizjes dhe dramë.

Ευχαριστήριος επιστολή

Λάβαμε από τον Σύλλογο Φίλων Παιδιών με Ειδικές Ανάγκες Κεντρικής Μακεδονίας ευχαριστήριο επιστολή για τους μαθητές και γονείς που ανταποκρίθηκαν στο κάλεσμά τους για ενίσχυση των σκοπών τους.
Με τη σειρά μας οι εκπαιδευτικοί του Σχολείου μας θέλουμε να ευχαριστήσουμε τους μαθητές μας και τους γονείς για το υψηλό αίσθημα κοινωνικής ευθύνης που τους διακρίνει και συνεισφέρουν, πολλές φορές από το υστέρημά τους, σε κάθε σχετική πρόσκληση που τους απευθύνεται.

Σημειώνουμε ότι, πέρα από το Σύλλογο Φίλων Παιδιών με Ειδικές Ανάγκες Κεντρικής Μακεδονίας, δόθηκε βοήθεια (οικονομική και υλική) μέσω του προγράμματος "Make a wish" σε παιδιά με νεοπλασματικές ασθένειες καθώς και σε οικογένειες και άτομα της περιοχή μας με προβλήματα διαβίωσης.

We received from the Association of Friends of Children with Special Needs Central Macedonia thank you letter for students and parents who responded to their call for strengthening their purposes.
With our range of teachers of our school we want to thank our students and parents for their high sense of social responsibility that distinguishes them and contribute many times their savings in every invitation addressed to them.
We note that, apart from the Association of Friends of Children with Special Needs Central Macedonia, help was given (financial and material) through the program "Make a wish" in children with neoplastic diseases as well as families and individuals in our region with welfare problems.

Ne kemi marrë nga Shoqata e Miqve të Fëmijëve me nevoja të veçanta Maqedonia Qendrore ju falenderoj letër për studentët dhe prindërit të cilët iu përgjigjën thirrjes së tyre për forcimin e qëllimeve të tyre.
Me gamën tonë të mësuesve të shkollës sonë ne duam të falënderojmë studentët tanë dhe prindërit për sensin e tyre të lartë të përgjegjësisë sociale që e dallon ato dhe të kontribuojnë shumë herë kursimet e tyre në çdo ftesë adresohen atyre.
Ne konstatojmë se, pavarësisht nga Shoqata e Miqve të Fëmijëve me nevoja të veçanta Central Macedonia, ndihmë është dhënë (financiare dhe materiale), përmes programit "të bëjë një dëshirë" në fëmijët me sëmundje neoplastike, si dhe familjeve dhe individëve në rajonin tonë me probleme sociale.

Γιορτή της Μητέρας

Η γιορτή της μητέρας ή ημέρα της μητέρας είναι κινητή εορτή προς τιμήν της μητέρας και γιορτάζεται κάθε χρόνο την δεύτερη Κυριακή του μήνα Μάη.

Εγκαθιδρύθηκε τον 20ό αιώνα και προέρχεται από το αγγλικό και το αμερικανικό κίνημα των γυναικών. Η Αμερικανίδα Ann Maria Reeves Jarvis διοργάνωσε για πρώτη φορά το 1865 ένα κίνημα με το όνομα Mothers Friendships Day και συναντήσεις με το όνομα Mothers Day Meetings, κατά τις οποίες οι μητέρες αντάλλασσαν απόψεις και εμπειρίες. Το 1870 η Julia Ward Howe διοργάνωσε μια εκδήλωση φιλειρηνικής συγκέντρωσης μητέρων με το σλόγκαν peace and motherhood με σκοπό, τα παιδιά να μην στέλνονται στον πόλεμο.

The Mother's Day or Mother's Day is a moveable feast in honor of the mother and is celebrated every year on the second Sunday of the month May.

Established in the 20th century and comes from the English and American women's movement. The American Ann Maria Reeves Jarvis was first organized in 1865 a movement named Mothers Friendships Day and meetings with named Mothers Day Meetings, during which the mothers exchanged views and experiences. In 1870 Julia Ward Howe organized a event peace-loving mothers concentration with the slogan peace and motherhood in order, children not sent to war. 

Dita e Nënës ose Dita e Nënës është një festë lëvizshme në nder të nënës dhe festohet çdo vit në të dielën e dytë të muajit maj.

E themeluar në shekullin e 20 dhe vjen nga anglisht dhe lëvizjes së grave Amerikan. Amerikane Ann Maria Reeves Jarvis u organizua për herë të parë në 1865 një lëvizje të quajtur Nënave Miqësi Dita dhe takimet me emrin Takimet Ditën e Nënave, gjatë së cilës nënat shkëmbyen mendime dhe përvoja. Në 1870 Julia Ward Howe organizua një Ngjarja nënat liridashës përqendrimi me paqe parullën dhe mëmësisë në mënyrë, fëmijët nuk dërgohen në luftë.

Εκπαιδευτική λειτουργία από τον Σεβασμιότατο κ.κ. Ιγνάτιο

Μια μοναδική εμπειρία έζησαν οι μαθητές του Σχολείου μας καθώς και του Αθανασάκειο Νηπιαγωγείου Πορταριάς και του Παιδικού Σταθμού Κατηχωρίου με την τέλεση εκπαιδευτικής Θείας Λειτουργίας στον Ι.Ν. του Αγίου Νικολάου Πορταριάς.

Μέσα σε κατανυκτικό κλίμα, στον αναστάσιμα στολισμένο ναό, η τέλεση της θείας λειτουργίας χοροστατούντος του Σεβασμιοτάτου, και των συλλειτουργούντων  αρχιμανδρίτου πατέρα Αγάθωνα, εφημέριου του Ι.Ν. Αγίου Νικολάου, και του αρχιδιακόνου πατέρα Καλλινίκου, εκτυλίχθηκε μπροστά στα μάτια των μαθητών η συμβολική παρουσία του Χριστού στη Γη, που με τις συνεχείς εξηγήσεις του  τους αποκάλυψε το μυστήριο της Θείας Ευχαριστίας. 

Πέρα από την εξήγηση κάθε σημείου της Θείας Λειτουργίας, των αντικειμένων και τι συμβολίζουν, των σε απλή γλώσσα ύμνων και κειμένων ήταν το πατρικό ύφος του Σεβασμιότατου και η απλότητα του που κέρδισε τις καρδιές μικρών και μεγάλων εκκλησιαζομένων. Άλλωστε κι ο ίδιος επέλεξε νάναι ο παππούς όλων μας που μας γεμίζει με την αγάπη του και δεν μας λησμονά στις προσευχές του. 

A unique experience lived our School's students and the Athanassakio Portaria Kindergarten and Kindergarten Katihori to commit educational Divine Liturgy in the Church St. Nicholas Portaria.

Within devout climate to Anastasios adorned temple, the celebration of the Holy Mass celebrated by His Eminence, and sylleitourgounton Archimandrite Father Agathon, curate of the Church St. Nicholas and Archdeacon Father Kallinikos, unfolded before the eyes of students to the symbolic presence of Christ on earth, with the constant explanations revealed the mystery of the Eucharist.

Apart from the explanation of each point of the Divine Liturgy, the objects and what symbolize, the plain language hymns and texts was the paternal style of Eminence and the simplicity that won the hearts of small and large church services. Besides, he himself chose voyage is the grandfather of all of us who fills us with his love and not forgetting us in his prayers.

Një përvojë unike jetuar nxënësit e shkollës sonë dhe Kopshti Athanassakio Portaria dhe Kopshti Katihori të kryejnë Liturgjinë Hyjnore arsimor në Kishë Shën Nikolla Portaria.

Brenda klimës devotshëm ndaj Anastasios tempull stolisur, kremtimin e Meshës së Shenjtë kremtuar nga Shkëlqesia e Tij, dhe sylleitourgounton të arkimandritit Ati Agathon, familltar e Kishës Shën Nikolla dhe Archdeacon Atë Kallinikos, shpalosen para syve të nxënësve në prani simbolike të Krishtit në tokë, me shpjegime të vazhdueshme zbuloi misterin e Eukaristisë.

Përveç shpjegimit të çdo moment të Meshës Hyjnore, objekteve dhe çfarë simbolizojnë, himnet gjuhë të thjeshtë dhe tekste ishte stil nga babai i Eminence dhe thjeshtësi që fitoi zemrat e shërbimeve të vogla dhe të mëdha të kishës. Përveç kësaj, ai vetë zgjodhi fluturim është gjyshi i të gjithë ne që na mbush me dashurinë e tij dhe nuk na harron në lutjet e tij.

Με τα παιδιά του 1ου Ειδικού Σχολείου Αγριάς ...

Με την ευκαιρία της γιορτής του Πάσχα  η χορωδία του Σχολείου μας επισκέφθηκε το Εδικό Σχολείο Αγριάς για να προσφέρει πασχαλινές λαμπάδες, που έφτιαξαν οι μαθητές της Στ τάξης με τη βοήθεια του Συλλόγου Γονέων, και να τους τραγουδήσει τραγούδια για την άνοιξη που επιμελήθηκε η μουσικός του Σχολείου μας Καραφέργια Κωνσταντίνα. 

Την ομάδα συνόδευσαν δάσκαλοι και γονείς του Σχολείου που είχαν την ευκαιρία να επισκεφθούν την σχολική μονάδα και να ενημερωθούν για το έργο που επιτελείται. Οι μαθητές μαζί με τους μαθητές του Ειδικού Σχολείου συμμετείχαν σε δραστηριότητες που εμψύχωσε η εκπαιδευτικός του Ειδικού Σχολείου Αγριάς Αλίκη Κουκουμβρή, για να ακολουθήσει η παρουσίαση των τραγουδιών. Ήταν μαι καταπληκτική εμπειρία και θέλουμε να ευχηθούμε το καλύτερο για τα παιδιά του Ειδικού Σχολείου Αγριάς.  

On the occasion of the feast of Easter the choir of our school visited the specially Agria School to offer Easter candles, which built by the students of the sixth grade with the help of the Parents Association, and to sing songs about spring curated by musician Our school Karafergia Constantina.

The group was accompanied by teachers and parents of the school who had the opportunity to visit a school and learn about the work being done. Oi students together with students of Special School participated in activities encouraged by the teacher of the Special School Agria Alice Koukoumvri for to follow the presentation of the songs. It was am amazing experience and we want to wish the best for the children of the Special School Agria.

Me rastin e festës së Pashkëve kori i shkollës sonë vizituar posaçërisht Agria shkollën e për të ofruar qirinj Pashkëve, të cilat të ndërtuara nga nxënësit e klasës së gjashtë me ndihmën e Shoqatës së Prindërve, dhe të këndojnë këngë për pranverën kuruar nga muzikanti Shkolla jonë Karafergia Konstantina.

Grupi u shoqërua nga mësuesit dhe prindërit e shkollës që kishte mundësi për të vizituar një shkollë dhe të mësojnë në lidhje me punën që po bëhet. Oi punë së bashku me nxënësit e Shkollës Speciale marrë pjesë në aktivitete të inkurajuar nga mësuesi i Shkollës Speciale Agria Alice Koukoumvri për të ndjekin prezantimin e këngëve. Ishte am përvojë e mrekullueshme dhe ne duam të uroj më të mirë për fëmijët e Shkollës Agria Speciale.

  

  

  

Solar eclipse

 

Την ηλιακή έκλειψη στις 20 Μαρτίου 2015, παρόλη την πρόσκαιρη χιονόπτωση καταφέραμε να παρακολουθήσουμε σε ένα μικρό άνοιγμα του συννεφιασμένου ουρανού και να φωτογραφίσουμε το φαινόμενο. Παράλληλα παρατηρήθηκε το φαινόμενο σε σύνδεση με το αστεροσκοπείο Γκρίνουϊτς όπου καλύφθηκε το 85% του ηλιακού δίσκου. Ήταν μια πρωτόγνωρη εμπειρία για όλους μας. Υλικό της φωτογράφισης θα σταλεί στο σχετική ομάδα του Open Discovery Space.

Solar eclipse on March 20, 2015, despite the temporary snowfall managed to watch a small opening of cloudy sky and to photograph the phenomenon. Alongside the phenomenon observed in connection with the Greenwich observatory where 85% of the solar disk covered. It was a new experience for us all. Gallery of photography will be sent to the relevant group of Open Discovery Space.

Eklips diellor më 20 mars 2015, përkundër reshjeve të borës së përkohshme arriti të shikojnë një hapje të vogël të qiellit me re dhe për të fotografuar fenomenin. Krahas fenomenit të vërejtur në lidhje me observatori Greenwich ku 85% e diskut diellor mbuluar. Kjo ishte një eksperiencë e re për të gjithë ne. Galeria e fotografisë do të dërgohet në grupin përkatës të Hapur Discovery hapësirë.

Πείραμα του Ερατοσθένη

 

Συμμετέχοντας το σχολείο μας στο δίκτυο "Eratosthenes Experiment" για δεύτερη συνεχή χρονιά,  πραγματοποίησε στις 19 Μαρτίου 2015 το προγραμματισμένο πείραμα. Το σχολείο μας αντάλλαξε στοιχεία μετρήσεων με το 1ο Δημοτικό Σχολείο Αργοστολίου, το 33ο Δημοτικό Σχολείο Βόλου, το Μειονοτικό Γυμνάσιο - Λύκειο Κομοτηνής και το 6ο Λύκειο Ξάνθης. Παρόλες τις δυσκολίες του καιρού το κρίσιμο διάστημα ο ήλιος μας έκανε τη χάρη και μας βοήθησε στην μέτρηση. 

By joining our school network "Eratosthenes Experiment" for the second consecutive year, held on March 19, 2015 the planned experiment. Our school exchange measurement data with the 1st Primary School of Argostoli, the 33rd Primary School of Volos, the Minority Middle School - Lyceum of Komotini and the 6th Lyceum of Xanthi. Despite the difficulties of the weather the period in the sun made us a favor and helped us to measure.

Duke u bashkuar rrjetit shkollor tonë "Eksperiment Eratosthenes" për të dytin vit radhazi, të mbajtur më 19 mars 2015 i eksperiment planifikuar. Këmbimit Shkolla jonë dhënave matje me Shkollën Fillore 1 e Argostoli, Shkollën fillore e 33 Volos, Shkolla e Mesme e Minoriteteve - Liceut të Komotinit dhe Liceut 6 të Xanthi. Me gjithë vështirësitë e motit periudhë në diell na bërë një nder dhe na ndihmoi për të matur.

Λίγα λόγια για το πείραμα ...

Το πείραμα του Ερατοσθένη βασίστηκε στη μέτρηση του ύψους του Ηλίου την ίδια ημερομηνία σε δύο διαφορετικές τοποθεσίες, καθώς και στην πεποίθηση του μεγάλου έλληνα μαθηματικού ότι ο Ηλιος είναι πολύ μακριά από τη Γη, τόσο ώστε οι ακτίνες του να φθάνουν στον πλανήτη μας σχεδόν παράλληλα. Από διηγήσεις ταξιδιωτών ο Ερατοσθένης έμαθε ότι στις 21 Ιουνίου, την ημέρα του θερινού ηλιοστασίου, ο Ηλιος καθρεφτίζεται στην επιφάνεια του νερού των πηγαδιών της πόλης Συήνης, αυτής που σήμερα οι Αιγύπτιοι ονομάζουν Ασουάν. Από την πληροφορία αυτή ο Ερατοσθένης συμπέρανε ότι η Συήνη βρίσκεται πάνω στον τροπικό του Καρκίνου, δηλαδή στον παράλληλο κύκλο με γεωγραφικό πλάτος 23,5 μοίρες. Το χαρακτηριστικό των τόπων που βρίσκονται στον τροπικό του Καρκίνου είναι ότι το μεσημέρι της 21ης Ιουνίου ο Ηλιος βρίσκεται στο ζενίθ, δηλαδή ακριβώς κατακόρυφα προς τα πάνω. Ετσι οι ακτίνες του διαδίδονται κατά μήκος των κατακόρυφων τοιχωμάτων των πηγαδιών, ανακλώνται στην επιφάνεια του νερού και επιστρέφουν προς την επιφάνεια, κάνοντας ορατό το είδωλό του σε έναν παρατηρητή που κοιτάζει από το στόμιο του πηγαδιού. 

Το μεσημέρι της ημέρας του θερινού ηλιοστασίου ο Ερατοσθένης μέτρησε το ύψος του Ηλίου στην πόλη στην οποία κατοικούσε, την Αλεξάνδρεια της Αιγύπτου. Η μέτρηση έγινε με τη βοήθεια ενός οβελίσκου, ο οποίος είναι το αρχαιότερο αστρονομικό όργανο στην ιστορία της επιστήμης. Το μήκος της σκιάς που ρίχνει ο οβελίσκος, διαιρεμένο με το ύψος του οβελίσκου, μας δίνει, όπως μάθαμε στο σχολείο, την εφαπτομένη της γωνίας του ύψους του Ηλίου. Η γωνία αυτή, η οποία από τη μέτρηση του Ερατοσθένη προέκυψε 7,2 μοίρες, είναι ίση (ως «εντός-εκτός και επί τα αυτά», όπως θυμούνται οι παλαιότεροι) με την επίκεντρη γωνία που σχηματίζουν δύο ακτίνες της Γης με άκρα τη Συήνη και την Αλεξάνδρεια, υπό την προϋπόθεση ότι οι δύο πόλεις έχουν το ίδιο γεωγραφικό μήκος, βρίσκονται δηλαδή στον ίδιο μεσημβρινό. Επειδή από τη γεωμετρία γνωρίζουμε ότι η απόσταση των δύο πόλεων, η ακτίνα της Γης και η γωνία που μέτρησε ο Ερατοσθένης συνδέονται με τη σχέση απόσταση/ακτίνα = 6,28x(7,2/360), η ακτίνα της Γης βρίσκεται αμέσως αν γνωρίζουμε την απόσταση των δύο πόλεων. Την εποχή του Ερατοσθένη, περί το 250 π.Χ., δεν υπήρχε ακριβής μέθοδος μέτρησης τόσο μεγάλων αποστάσεων. Σύμφωνα με την παράδοση, ο Ερατοσθένης ανέθεσε σε επαγγελματίες βαδιστές να την υπολογίσουν, και το αποτέλεσμά τους το συνέκρινε με τις εκτιμήσεις αρχηγών καραβανιών. Το τελικό του αποτέλεσμα ήταν ότι η απόσταση Αλεξάνδρειας- Συήνης ισούται με 5.000 στάδια, οπότε η ακτίνα της Γης προκύπτει ίση με 252.000 στάδια. 

Για να μπορέσουμε να εκτιμήσουμε την ακρίβεια της μέτρησης του Ερατοσθένη, θα έπρεπε να γνωρίζουμε πόσο είναι το μήκος ενός σταδίου σε μέτρα, καθώς και κατά πόσο αληθεύουν οι δύο υποθέσεις του Ερατοσθένη, δηλαδή ότι η Συήνη έχει γεωγραφικό πλάτος 23,5 μοίρες και ότι Συήνη και Αλεξάνδρεια βρίσκονται στον ίδιο μεσημβρινό. Μια ματιά σε έναν σύγχρονο χάρτη δείχνει ότι και οι δύο υποθέσεις ήταν λανθασμένες, αλλά το λάθος δεν ήταν μεγάλο: το γεωγραφικό πλάτος της Συήνης είναι 24,1 μοίρες, ενώ τα γεωγραφικά μήκη των δύο πόλεων διαφέρουν μόνο κατά μία μοίρα. Επομένως η βασική πηγή σφάλματος είναι το μήκος ενός σταδίου σε μέτρα. Θα έλεγε κανείς ότι έχουν διασωθεί πολλά αρχαία στάδια, οπότε δεν έχουμε παρά να μετρήσουμε πόσο μήκος έχει ένα από αυτά. Δυστυχώς τα στάδια δεν είχαν το ίδιο μήκος σε όλες τις περιοχές της αρχαίας Ελλάδας. Αν υποθέσουμε ότι ο Ερατοσθένης εννοούσε αττικά στάδια των 185 μέτρων, τότε το αποτέλεσμά του δίνει για την ακτίνα της Γης 7.400 χιλιόμετρα, τιμή 16% μεγαλύτερη από την πραγματική. Αν όμως εννοούσε αιγυπτιακά στάδια, πράγμα που είναι και το πιθανότερο, τότε κατά τον Ερατοσθένη η ακτίνα της Γης είναι 6.316 χιλιόμετρα, μόλις 1% μικρότερη από την πραγματική, που σήμερα γνωρίζουμε ότι είναι 6.366 χιλιόμετρα! 

About the experiment ...

The experiment of Eratosthenes was based on the measurement of the height of the Sun the same day in two different locations, and the conviction of the great Greek mathematician that the Sun is very far from Earth, so that the rays to reach the planet almost parallel. From stories of travelers Eratosthenes learned that on June 21, the day of the summer solstice, the sun is reflected on the surface of the water of the city wells Syinis, that now the Egyptians call Aswan. From this information Eratosthenes concluded that Syini lies on the Tropic of Cancer, that is the parallel circle with latitude 23.5 degrees. The characteristic of sites located on the Tropic of Cancer is that at noon on June 21 the sun is at the zenith, that is exactly vertically upwards. Thus rays propagate along the vertical walls of the wells, are reflected at the water surface and back to the surface, making visible his reflection to an observer looking from the mouth of the well.

At noon on the day of the summer solstice Eratosthenes measured the height of the Sun in the city in which he resided, Alexandria, Egypt. The measurement was made using a tang, which is the oldest astronomical instrument in the history of science. The length of the shadow cast by its obelisk, divided by the height of the obelisk, gives us, as we learned in school, the tangent of the angle of the height of the sun. This angle, which by measuring Eratosthenis showed 7.2 degrees, is equal (as "on-off and on those" as remember older) with the central angle formed by two radii of the Earth with its ends Syini and Alexandria, provided that the two cities have the same longitude and are therefore on the same meridian. Because of the geometry we know that the distance between the two cities, the radius of the Earth and the angle measured Eratosthenes associated with the relationship distance / radius = 6,28x (7,2 / 360), the radius of the Earth is immediately if we know the distance between the two cities. At the time of Eratosthenes, around 250 BC, there was no accurate method of measuring such large distances. According to tradition, Eratosthenes commissioned walkers professionals to calculate, and their effect compared with the estimates Heads caravan. The final result was that the distance of Alexandria Syinis equals 5,000 steps, so the radius of the Earth resulting equal to 252,000 steps.


In order to assess the accuracy of measurement of Eratosthenes, we should know how much is the length of a stage in meters and how true the two cases of Eratosthenes, namely that Syini has latitude 23.5 degrees and that Syini and Alexandria are on the same meridian. A look at a modern map shows that both assumptions were wrong, but the error was not large: the latitude of Syinis is 24.1 degrees, while the longitudes of the two cities differ only by one degree. Therefore the main source of error is the length of a step in meters. One could say that they have preserved many ancient stages, so we only have to measure how long is one of them. Unfortunately stages were not the same length in all regions of ancient Greece. Assuming that Eratosthenes meant Attic steps of 185 meters, the result gives the radius of the Earth 7400 km, price 16% higher than the actual. But if he meant Egyptian stage, which is likely, then by Eratosthenes radius of Earth is 6316 km, only 1% less than the real, we now know that it is 6366 kilometers!

Rreth eksperimentit ...

Eksperimenti i Eratosthenes është bazuar në matjen e lartësisë së Diellit të njëjtën ditë në dy lokacione të ndryshme, si dhe bindja e matematikan i madh grek se Dielli është shumë larg nga Toka, në mënyrë që rrezet për të arritur planet pothuajse paralel. Nga tregimet e udhëtarëve Eratosthenes mësuar se më 21 qershor, ditën e solsticit veror, dielli është pasqyruar në sipërfaqen e ujit të puseve të qytetit Syinis, që tani Egjiptasit quajnë Aswan. Nga ky informacion Eratosthenes arriti në përfundimin se Syini shtrihet në Tropiku i Gaforres, që është rrethi paralele me gjerësi 23,5 gradë. Karakteristikë e vendeve të vendosura në Tropiku i Gaforres është se në mesditë më 21 qershor dielli është në zenit, që është pikërisht vertikalisht lart. Kështu rrezet përhapur përgjatë mureve vertikale të puseve, janë pasqyruar në sipërfaqen e ujit dhe përsëri në sipërfaqe, duke e bërë të dukshme reflektimin e tij për një vëzhgues në kërkim nga goja e mirë.

Në mesditë në ditën e solsticit veror Eratosthenes matur lartësinë e Diellit në qytetin në të cilin ai e banuar, Alexandria, Egjipt. Matja është bërë duke përdorur një erë e fortë, e cila është instrumenti më i vjetër astronomik në historinë e shkencës. Gjatësia e hedhur hije nga obelisku i saj, pjesëtuar me lartësinë e obelisk, na jep, siç kemi mësuar në shkollë, tangjent e kënd e lartë të diellit. Ky kënd, e cila duke matur Eratosthenis tregoi 7,2 gradë, është e barabartë (si "on-off dhe mbi ata" si të kujtuar më të vjetër) me kënd qendror i formuar nga dy radii e Tokës me skajet e saj Syini dhe Alexandria, me kusht që dy qytetet kanë të njëjtin gjatësi dhe janë në të njëjtin meridian. Për shkak të gjeometrisë ne e dimë se distanca mes dy qyteteve, rrezja e Tokës dhe kënd matur Eratosthenes i lidhur me marrëdhënie distancë / rrezja = 6,28x (7,2 / 360), rrezja e Tokës është menjëherë në qoftë se ne e dimë distanca ndërmjet dy qyteteve. Në kohën e Eratosthenes, rreth 250 pes, nuk kishte asnjë metodë të saktë të matur distancat tilla të mëdha. Sipas traditës, Eratosthenes porositur rrethoresh profesionistë për të llogaritur, dhe efekti i tyre në krahasim me vlerësimet kokat karavan. Rezultati përfundimtar ishte se distanca e Aleksandrisë Syinis është e barabartë me 5000 hapa, kështu që rrezja e Tokës rezultuar e barabartë me 252.000 hapa.


Për të vlerësuar saktësinë e matjes së Eratosthenes, ne duhet të dimë se sa është gjatësia e një faze në metra dhe sa e vërtetë të dy rastet e Eratosthenes, domethënë që Syini ka gjerësi 23,5 gradë dhe se Syini dhe Aleksandri janë në të njëjtën meridian. Një vështrim në një hartë moderne tregon se të dy supozimet e kishin gabim, por gabimi nuk ishte i madh: gjerësi e Syinis është 24,1 gradë, ndërsa longitudes e dy qyteteve të ndryshojnë vetëm nga një shkallë. Prandaj burimi kryesor i gabimit është gjatësia e një hap në metra. Dikush mund të thotë se ata kanë ruajtur shumë faza të lashta, kështu që ne vetëm duhet për të matur se sa kohë është një prej tyre. Për fat të keq fazat nuk ishin të njëjta gjatësi në të gjitha rajonet e Greqisë së lashtë. Duke supozuar se Eratosthenes menduar hapat papafingo e 185 metra, rezultat i jep rrezja e Tokës 7400 km, çmim 16% më të larta sesa aktual. Por në qoftë se ai do të thotë fazë egjiptiane, e cila është e mundshme, atëherë me Eratosthenes rrezja e Tokës është 6316 km, vetëm 1% më pak se reales, ne tani e dimë se ajo është 6366 kilometra!