Eratosthenes and His Measurements

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What was Eratosthenes' estimated circumference of the Earth?

20,000 miles (32,000 km)
25,000 miles (40,000 km) (correct)
30,000 miles (48,000 km)
35,000 miles (56,000 km)

At which location was Eratosthenes the chief librarian?

Library of Alexandria, Egypt (correct)
Library of Cyrene, North Africa
Library of Rome, Italy
Library of Athens, Greece

In Eratosthenes' calculation, what fraction of the Earth's circumference was the distance between Alexandria and Swenet?

1/100th
1/50th (correct)
1/10th
1/25th

What was the primary method Eratosthenes used to calculate the Earth's circumference?

Comparing the angle of shadows at two different locations at the same time. (A) Signup and view all the answers

Which of the following terms is Eratosthenes credited with coining?

Geography (B) Signup and view all the answers

Besides calculating the Earth's circumference, which mathematical method is attributed to Eratosthenes?

Developing a reliable method for finding prime numbers. (C) Signup and view all the answers

What was the approximate distance between Alexandria and Swenet (Syene) that Eratosthenes used in his calculation?

500 miles (A) Signup and view all the answers

What practical application did Archimedes' principle of buoyancy enable?

Calculating the volume of irregularly shaped objects by submerging them in water. (A) Signup and view all the answers

Which of the following calculations relates to information found in the illustration, but not to Eratosthenes' work?

Determining that volume of a sphere is two-thirds of a cylinder. (C) Signup and view all the answers

About how many years ago did Eratosthenes perform his famous measurements?

Approximately 2200 years ago (B) Signup and view all the answers

King Hieron II tasked Archimedes with determining what about his crown?

Whether the crown was made of pure gold, as suspected. (A) Signup and view all the answers

Given Eratosthenes' methodology and findings, what is most directly measured to enable the computation of Earth's circumference?

The angular difference of shadows at two distant points. (C) Signup and view all the answers

Besides using it to pump water from boats, in what other setting might Archimedes have encountered the Archimedes screw?

While observing irrigation techniques in Egypt. (B) Signup and view all the answers

What aspects of Archimedes's achievements were suggested to be emphasized on his tombstone?

His discovery of the principle of buoyancy. (A) Signup and view all the answers

What was the main function of the Claw of Archimedes during the siege of Syracuse?

To lift enemy ships out of the water and capsize them. (C) Signup and view all the answers

Approximately when did Archimedes die?

212 BCE (B) Signup and view all the answers

What does Archimedes mean when he says, 'Give me a lever and a place to stand, and I will move the Earth.'?

With the correct force and leverage any object can be moved. (C) Signup and view all the answers

What kind of system did Archimedes build to help launch ships?

A lever and pulley system. (A) Signup and view all the answers

Who was the 2,000-man ship a gift for?

Ptolemy III. (A) Signup and view all the answers

What are 'BCE' and 'CE'?

Before common era and common era, respectively. (C) Signup and view all the answers

Which of the following represents the most significant impact of Archimedes' work on modern science and engineering?

His theoretical frameworks in geometry and mechanics laid groundwork for future scientific and engineering advancements. (B) Signup and view all the answers

How did Archimedes' social and political context in Syracuse likely influence his scientific pursuits?

The patronage of King Hieron II provided him with resources and freedom to explore theoretical and practical problems. (C) Signup and view all the answers

What distinguishes Archimedes' approach to mathematics and science from that of his contemporaries?

His integration of theoretical mathematics with practical inventions and engineering solutions. (B) Signup and view all the answers

How does Archimedes' work On Floating Bodies demonstrate his understanding of physics?

It outlines the principle of buoyancy and applies it to explain the behavior of objects in fluids. (C) Signup and view all the answers

In what way did Archimedes' calculation of the number of grains of sand in the universe contribute to mathematical thought?

It pioneered a method for expressing and manipulating very large numbers, expanding the scope of mathematical notation. (B) Signup and view all the answers

How did Archimedes' early studies in Alexandria shape his later work in Syracuse?

They provided him with a strong foundation in mathematics and exposure to other brilliant scholars. (D) Signup and view all the answers

What distinguishes Archimedes' approach to geometry from that of earlier mathematicians?

He developed methods for calculating the volumes of complex geometrical solids, like spheroids. (D) Signup and view all the answers

How did Archimedes' invention of the Archimedes screw impact daily life in ancient times?

It provided a more efficient method for irrigating fields and dewatering mines. (D) Signup and view all the answers

What was a key characteristic of the ship Syracusia, which Archimedes designed?

It was a marvel of engineering and massive in scale. (A) Signup and view all the answers

How did Archimedes' method for approximating $\pi$ differ from previous attempts?

He used more complex geometric shapes to more accurately bound the area/circumference of a circle. (A) Signup and view all the answers

Archimedes

One of the greatest ancient mathematicians and theoreticians.

Syracusia

A massive ship designed by Archimedes for Ptolemy III.