History and math. Нand in hand. Book 1. Ancient World. 50 mathematical tasks for students based on historical events. Ancient Rome, Greece, Egypt and Persia. Dmitry Moskovets

soldiers took part in the battle?

      G.11. A little about Theseus21, Aegeus and the Minotaur22

      Having defeated the Minotaur, Theseus, as depicted in the famous myth and cartoon, went home to Athens. Today, in Crete, a ferry from Heraklion, near the Palace of Knossos, runs to Athens in the evening at 21:00. It arrives at 6:00. Could Aegeus have seen the black sail of Theseus’ ship if Theseus sailed at the same time as the modern ferry? Theseus’ ship moved 6 times slower. The distance to Athens is 306 km.

      Ancient Rome

      We could talk for hours about ancient Rome, and even today, many scholars still study the great history of the Roman Empire. We won’t go deeply into the details here. Instead, we’ll look at some tasks and think about the Empire’s main historical events.

      THE FIRST PUNIC WAR

      The «First Punic War» is the war between Carthage and the Roman Republic. It started in 264 BC and lasted for 23 years ending with the victory of the Romans.

      R.1. Legions are longing for the sea

      At the start of the First Punic War, Carthage reigned supreme as the dominant maritime power, and Roman light ships couldn’t inflict any significant damage to the Carthaginian quinqueremes23. However, by an accident of fate, one quinquereme was thrown on land. The delighted Romans took the ship and carefully disassembled the vessel. They copied the design and constructed a mighty Roman fleet of 100 quinqueremes and 20 triremes24.

      How many: legions25, maniples, centurias the new fleet could carry?

      R.2. Rowing is an honorable occupation

      In the era of the Roman Republic, rowers were highly respected. After the Roman fleet was built, rowers hired and trained tirelessly. How many rowers enrolled in the fleet? The size of the fleet is mentioned in the previous task.

      R.3. Toward each other

      The distance between Carthage and Sicily26 was 213 km. The First Punic War was still going on, and a fast quinquereme sailed from Lilibey to Carthage with an urgent message. Meanwhile, a small fleet of various ships with reinforcements and provisions set sail for Sicily. How long will it take for the fast ship to meet the fleet if the fleet’s speed is 4 knots and the quinqireme’s is 6 knots? Sailors measure everything in miles. One mile is 1853 m, and a knot – measure of speed, – equals 1 mile per hour.

      R.4. How many ships did disappear and where did they go?

      In ancient times they went, as a rule, to the seabed. There were several reasons why they sank. Firstly, they could have been damaged in battle, or, simply because of their poor state due to the crew’s negligence, could start leaking. However, the primary reason for ships’ disappearance was Neptune’s27 wrath or forces of nature, to put it in contemporary terms.

      1,200 ships of the First Punic War didn’t escape this fate. Carthage lost five out of every twelve ships, while the Romans lost seven of every twelve. In total, who lost more ships and by how many?

      The task can be dealt with in two ways, and, of course, we might try to assess whether there were many ships in the ancient fleet compared to modern times.

      THE SECOND PUNIC WAR

      The Second Punic War lasted since 218 to 201 BC in Italy, Spain and modern Tunisia. Many historians described the war, and many battles were included into military texts and may fascinate even today. For example, the eminent Roman historian Titus Livius28 wrote a book about it called The War with Hannibal. 2,000 years ago.

      R.5. The trophies of Saguntum29

      The Second Punic war began in 219 BC when Hannibal30 sieged Saguntum. His victorious army captured 2,925 pounds of silver.

      Hannibal’s army consisted of Nubian horsemen, Spanish infantry, Carthaginian warriors, tribes from southern Spain, and Balearic slingers31. The ratio of their numbers in the army was 1:2 2:1:0.5.

      Hannibal made a just decision to divide everything equally between the soldiers. There were 1,000 Balearic slingers in the army. How many asses (ancient Roman currency) did each soldier get? One denarius was worth 10 asses, and one pound is 72 denarii.

      R.6. Swift Carthaginian spy

      The Roman consul decided to send several triremes to support the armies fighting in Spain, near Massalia, (modern Marseille in France). The fleet was not far from Pompeii32, and Gannon, a cunning Carthaginian spy, found out about this. To warn Hannibal’s army, he would need to travel faster than the Roman triremes. How quickly does Gannon need to travel by land if the distance between Pompeii and Massalia is 791 km by sea? By land, the spy needs to pass through Rome and Genoa. The distance between Pompeii and Rome is 173 km, from Rome to Genoa – 403 km, and from Genoa to Massalia – 346. The average speed of trireme is 5 km per hour. Well, one cannot always have a tailwind! The spy needs to sleep at least 6 hours a day. Otherwise, he might lose his vigilance and get captured by the valiant Praetorians33.

      R.7. The first battle of the Second Punic War

      In November 218 BC, Hannibal’s troops approached the Ticinus River. Simultaneously, from Italy, Scipio’s34 troops approached the same river. The first battle took place near this place. From Carthage’s side, only its cavalry took part in the battle. However, the Romans used both cavalry and light infantry, velites35. Hannibal had 6,000 cavalry units. From the Roman side, the cavalry was 100 units more than half of the Carthaginian forces. Moreover, the infantry was 20% more than Hannibal’s cavalry. In total, how many soldiers took part in the battle?

      R.8. The Battle of Trebbia or how to win allies