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
of them than in the Battle of Thermopylae? The population of the Empire equaled 50 million.
P.5. The King`s «eyes» and «ears»
A whole army of spies worked for Cyras II the Great11. They were keeping an eye on everything that was going on in the Empire. Some even believe that the security servicemen lined up in a chain from the capital to the outskirts and shouted the latest news to the next in the chain.
It took thirty days for an army to march from the border of the Empire, but the king could know it was approaching in just one day because of his line of spies.
See whether this is possible if the army moves 8 hours a day, the king`s «ears» stand every 200m and the speed of sound 330 m/s. (for convenience sake, let it be 300 m/s). The speed is 5 km/h.
Let’s assume that it takes 10 second to convey the message from one spy to another.
P.6. Anniversary of Cyrus II.
Have you ever attended the king’s anniversary? No? But they are still held. Iran, for example, celebrated the 2,500 anniversary of the death of King Cyrus II in 1971. How long did Cyrus live, if he came to the throme in 559 BC, when he was 31 years old?
Ancient Greece
Ancient Greece was home to many mathematicians, philosophers, sculptors, and, of course, military leaders. It is also a place that gave democracy to the world.
G.1. Athens is the capital of Greece
The history of Athens dates back centuries. It is difficult to tell exactly who and when founded Athens. The period of greatest prosperity of Athens was the 5th century BC. Naming the exact number of population also proves to be a difficult task – the census was not conducted, and no one saw slaves as equal men: they were seen as property. Aside from slaves, there were wealthy citizens in Athens (slave owners, artisans), demos (poorer citizens), metics (migrants). Let’s assume the following: there were 90,000 slaves in Athens (historians believe this number to be 75—100 thousand) and settlers accounted for 20% of the population. There were as many citizens as slaves and metics combined. How many people lived in Athens?
G.2. Alexander the Great – a builder?
Let’s add together the number of cities founded by Alexander the Great12 and the number of modern countries where those cities are located. (Half the number of the cities) Then, add another 1/10 of the total number of cities and states, and we’ll get the number of years Alexander the Great lived. By the way, he used to name his cities Alexandria. 3/5 of the cities founded still exist, but have changed their names, all except for one. How many cities, founded by the King of Macedonia, have survived to this day? Alexander the Great was born in 356 BC and died in 323 BC.
G.3. How many students were in Pythagoras’s school?13
«Tell me, famous Pythagoras14, how many students attend your school and listen to your speeches?»
«I’ll tell you,» the philosopher replied. «Half of my students study mathematics, a fourth of them – music, and a seventh of them have taken a vow of silence. Additionally, there are three women.
How many students are there in Pythagoras’s school? They were also called «Pythagoreans».
G.4. The Battle of Gaugamela, and Darius III’s15 miscalculation
Like many generals, Darius III had initially underestimated his enemy. Therefore, he hastily gathered war elephants, 200 chariots, infantry and cavalry and recklessly rushed into battle. The Macedonians immediately captured the elephants, and Alexander’s 7,000 horsemen and 40,000 infantry put the Persians to flight.
Indeed, some historians claim that Darius’s army outnumbered the Macedonians by ten to one. However, there are more conservative estimates. How many horses took part in the battle if a chariot was harnessed with two 2 horses, and Darius had 8 thousand more cavalry than Alexander had infantry? Remember that this event took place on October 1, 331 BC, after which the Achaemenid Empire ceased to exist.16
G.5. Calendars and sport
As you may have already guessed, we are talking about the Olympics. From the first Olympics the ancient Greeks began to count years using their calendar. Calculate in what year, according to the ancient Greek calendar, this book was published, if the first Olympics took place in 776 BC.
G.6. The Battle of Thermopylae
The Battle of Thermopylae took place in September 480 BC. This unique battle is notable for an almost 40-fold superiority of the Persian forces. If the Greeks had 200 soldiers less, then, according to Herodotus17, the Persian army would have been 40 times larger than the Greek. As you know, the Spartans, like the rest of the Greeks, fought to the death. Only the betrayal of a local resident allowed the Persians to attack the rear of the Greek positions. Leonidas foresaw this and therefore sent part of his army back. After 4,000 Greeks were killed and the Persians lost 20,000, the Persian army became 150 times larger than the Greek. How many soldiers were in the Persian army?
G.7. Pericles18, the father of Athenian democracy, or what did Pythagoras have to do with him?
In history, it is crucial to what came first: Ancient Rome or the Republic of Venice, Caesar or Dmitry Donskoy? After that, there should no confusion about who was born first: Archimedes, Pythagoras or Pericles. All three of them were Greeks and prominent personalities. Pythagoras was born first in 570 BC. He lived 5 years longer than Archimedes. Archimedes lived 10 years longer than Pericles. If we add up all the years they lived, we get 220 years. Pericles was born 4 years after the death of Pythagoras. How many years passed between Pericles’ death and Archimedes’ birth, if 358 years passed between the birth of Pythagoras and the death of Archimedes?
G.8. The Peloponnesian War or Sparta versus Athens
As usual, the Peloponnesian War started because Athens wanted the Spartans to be just like them, and the Spartans wanted the opposite. The war lasted from 431 to 404. BC. Historians distinguish two periods of the war: the Archidamian War and the Deceleian War. Between them, there was the «Peace of Nicias» that lasted for six years. How long did the Archidamian War last, if it was a year longer than the Deceleian War did?
G.9. The Parthenon as tremendous historical legacy
Dedicated to Athena, the Parthenon’s construction on the Acropolis19 lasted from 447 to 438 BC. Even though it was burned down and partially destroyed, it draws attention with its columns’ straight lines. To achieve this, ancient architects curved the straight lines and even tilted some of the columns around the temple’s perimeter. There are 9 more columns on the east side than on the south. In total, there are 16 columns on the south and north sides. How many columns are there along the temple’s perimeter?
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.