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 2 стр.


G.10. The Battle of Marathon or how the Marathon races were born

On September 12, 490 BC, not far from Athens (42 km), a battle between the Persians and the Greeks took place. This was the first significant victory of the Greeks over the Achaemenid Empire. The Persian forces were 160% larger than the Greek army. The Athenians made up 90% of the Greek army. The Greeks won, and a messenger ran from Marathon to Athens. Upon his arrival in Athens, he fell dead in the square with the words, «Rejoice, Athenians, we have won!»20 After his epic run, the distance he ran (42 km) became known as the «Marathon».

How many Athenians were in the Greek army, if, in total, 36 thousand 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 wont go deeply into the details here. Instead, well look at some tasks and think about the Empires 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 couldnt 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 fleets speed is 4 knots and the quinqiremes 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 crews negligence, could start leaking. However, the primary reason for ships disappearance was Neptunes27 wrath or forces of nature, to put it in contemporary terms.

1,200 ships of the First Punic War didnt 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.

Hannibals 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 Hannibals 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, Hannibals troops approached the Ticinus River. Simultaneously, from Italy, Scipios34 troops approached the same river. The first battle took place near this place. From Carthages 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 Hannibals cavalry. In total, how many soldiers took part in the battle?


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

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

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