Playing by Eratosthenes's rules

On a recent visit to the Bibliotheca Alexandrina, Nader Habib finds out how to measure the circumference of the earth

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Clockwise from top left: the first map of the world; video conference with AUC, Aswan and French students; experimenting with Eratosthenes's ways of measuring the earth; a drawing depicting how he did his measurement; Omar Fekri; Shaymaa El-Sherif addressing the audience; Samir Sadek among his students; calculating the circumference; Eratosthenes's way of measuring the earth

On 21 June this year it was time for the Bibliotheca Alexandrina to measure the circumference of the earth. A re-enactment of the original feat, carried out by Eratosthenes (b 276 BCE), third director of the original Alexandria Library in antiquity, for the past nine years, the Bibliotheca has been inviting students to attend the re-enactment that is held each year on the summer solstice. This year, nearly 450 people gathered for this day of scientific celebration, organised by the library's Planetarium.

Sitting in a hall full of teenagers, one expects random noise and spontaneous energy. But not this time. As Shaymaa El-Sherif, unit chief of the francophone library at the Bibliotheca, took the podium you could hear a pin drop. Her presentation of this almost incredible piece of scientific research was so riveting that the middle-school students listened in silence, as if in a trance.

El-Sherif wrote her PhD thesis about the world view of Eratosthenes as seen in fiction. In her lecture, she mentioned that Eratosthenes was born in Cyrene, in today's Libya, in 276 BCE. Cyrene at that time was almost as well-known as Alexandria or Athens. He studied in Athens and then settled in Alexandria to teach and research.

Shedding light on Alexandria's history, El-Sherif noted that Alexander the Great did not build Alexandria. Instead, the architect Dinocrates did so on the orders of Ptolemy I, who ruled Egypt after Alexander's death. A student of Aristotle, Ptolemy prided himself on patronising science and scientists, and when he acceded to the Egyptian throne he asked Straton of Lampsakos, a prominent scientist with encyclopaedic knowledge, to teach his son.

The son grew up to take the name of Ptolemy II Philadelphus, or "lover of his sister". A statue of Ptolemy II stands at the Bibliotheca's entrance on Port Said Street in Alexandria in recognition of his role in establishing the original library. For tutoring his son, Ptolemy I rewarded Straton with 80 talents, or the equivalent of two tonnes of silver.

Ptolemy II was just as passionate about science as his father, and it is he who put the final touches to the ancient library. His son Ptolemy III Euergetes (his name means "good-doer") is the one who hired Eratosthenes. Impressed by what he heard of the latter's brilliance, Ptolemy III offered the young scientist, living in Athens at the time, the chance to become resident scientist in Alexandria and tutor to his son. The latter would later rule under the name of Ptolemy IV Philopater (his name translates as "father-loving").

In 245, Eratosthenes, still in his early 30s, became a scientist at the mouseion, Alexandria's Temple of the Muses, which was also the city's top institution of learning and included the famous library. It was a high-ranking job with many perks, including unfettered access to the royal family.

Before long, Eratosthenes became the mouseion's most important scientist, and, when Apollonius of Rhodes, second director of the library died shortly afterwards, Ptolemy III issued a decree appointing Eratosthenes in his place. It was a position that Eratosthenes kept for 40 years. According to El-Sherif, Eratosthenes owed his long tenure to his tendency to steer clear of politics and focus on his work and research.

Eratosthenes coined the word geography, which he would have pronounced geographicus. He is also credited with drawing up the first map of the earth, which he based on information available in Alexandria at the time. He considered cartography, or the science of mapping, to be an independent branch of knowledge, and he drew a full map of the River Nile, an achievement that brought him considerable criticism from his contemporaries as during his time the Nile was thought to originate not on earth but in heaven.

Eratosthenes was also keen to provide an accurate chronology of historical events, beginning with Homer's Trojan War. This too brought him criticism, as Homer's poems were rarely analysed at the time and instead were treated as kind of semi-divine texts.

As well as measuring the circumference of the earth and proving that it was round, Eratosthenes also measured the distances from earth to both the sun and the moon. In mathematics, he is credited with inventing a method for identifying primary numbers known as the "sieve of Eratosthenes". During his time as director of the library, a sister institution was created at the Serapium in today's Kom Al-Shoqafa. This library was to become a centre of learning in Roman times after the main branch was destroyed.

Eratosthenes became blind in 195 and died a year later aged 82. All of his writing has been lost, and we only know of his work from later scholars such as Strabo, who lived 100 years later and discussed his research at length. The reason we know about his method of measuring the earth is because Cleomides describes it in detail in his book entitled The Circular Motion of Celestial Bodies.

Following El-Sherif's description of the life and times of Eratosthenes, Omar Fikri, a senior official at the Planetarium, took to the podium. He produced a globe made of plastic, and, jokingly placing it under his foot, asked the audience if anyone was there against their will. He then proceeded to link the political events in Egypt and Libya to Eratosthenes's time.

According to Fikri, what matters most about Eratosthenes's ideas is the deductive method he uses in scientific experiments. Just like his friend Archimedes, Eratosthenes was interested in coming up with innovative solutions to scientific problems.

The story about Archimedes and the bath followed: Hiero, king of Syracuse, once ordered a crown of gold weighing 750 grammes to be made. He then suspected that the goldsmith may have stolen some of the gold and asked Archimedes to investigate the matter without damaging the crown. The scientist went to take a bath, stepped inside the tub, and came out shouting eureka, or "I've found it."

The theory he had found, later used to test the real weight of the crown, was that the amount of water an object displaces depends on its volume.

Back with Eratosthenes's theories, Fikri reminded the audience that the earth revolves around an axis that is tilted by 23.44 degrees. The tilt explains why we have four seasons instead of two. The sun becomes vertical above the tropic of cancer on 21 June, a fact that Eratosthenes used to measure the earth's circumference.

Eratosthenes knew that there was a well in the city now called Aswan in which you could see the light all the way to the bottom at noon on that particular day. In Alexandria, where he lived, obelisks would cast short shadows on the ground at the same moment. By measuring the shadows, which were tilted by seven degrees, he was able to deduce the circumference of the earth.

He knew that the distance between Alexandria and Aswan was nearly 800km, and that this distance matched a tilt equalling seven degrees. His next question was: which distance would produce a tilt of 360 degrees? The answer he came up with was verified, with only a tiny discrepancy, by modern science.

Fikri told the audience to go to the outdoor plaza and repeat the experiment. Sometime between 11:50 and 12:10, we all tried to stand pencils vertically on pieces of paper and measure the tilt of the shadow, or the angle created by the shadow in comparison to the vertical pencil. This was the first step towards applying Eratosthenes's equation: the angle of the sun/360 = distance to the tropic of cancer/earth's circumference.

Reda Qandil is a Planetarium official and the organiser of the summer solstice event. "We have been preparing for this celebration since December," she told Al-Ahram Weekly, noting that this was the ninth such event held by the library. Qandil had made sure to supply the audience with graph paper, protractors and compasses to measure the tilt of the sun's axis. The findings of the audience were relayed to Aswan, where another team of students replicated the experiment. Students in Spain and Greece were connected to Egypt on video links to witness the moment.

"Nine years ago we started this event with a very small number of students, but now we have 500 participants or more," Qandil said. She added that the Bibliotheca was involved in promoting science clubs all over the country, in which participants could share in the library's science programmes.

"We train teachers in cooperation with the Ministry of Education in order to create a scientific corps in the schools," she added.

Ahmed Tareq Refaai, a seventh-grade student, was helping other students conduct the experiment in the plaza. "I supervise 20 students divided into four groups. I make sure that they all have enough water to drink in order not to get dehydrated in the heat, and I guide them through the experiment."

Aya Mohamed Riad, a student at the Al-Horreya School, was busy measuring the shadow on her piece of paper. When asked about her progress, she said that she intended to study science when she went to college.

Samir Sadeq Yaqoub, deputy principal at the Youssef Abbas School, was pleased with the attendance. "It's great to see students take part in a science experiment such as this," he said, voicing hope that education in Egypt would improve after the 25 January Revolution.

Waiting for the outcome of the experiment with obvious eagerness, Mustafa Talaat, 12, said that science could be just as exciting as sport.

Then the results were announced. The students, on average, had estimated the circumference of the earth at 42,353 kilometres, more than five per cent off the real figure of 40,075.