History of Mathematics: Ancient Greece

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Questions and Answers

What was the primary method used by Archimedes to compute the area of various shapes?

  • Exhaustion method (correct)
  • Geometric progression method
  • Induction method
  • Differential method

Which of the following was NOT one of Archimedes' areas of expertise?

  • Mathematics
  • Physics
  • Astronomy
  • Biology (correct)

What is the approximate value of π that Archimedes showed?

  • Ï€ ∈ [3 10/71, 3 10/70] (correct)
  • Ï€ ∈ [3 1/4, 3 1/3]
  • 3.14
  • Ï€ ∈ [3 1/7, 3 10/71]

What was the name of the institution where Archimedes is believed to have studied or visited?

<p>The Museum (A)</p> Signup and view all the answers

What is the name of the concept that later developed from Archimedes' method of exhaustion?

<p>Modern integration (B)</p> Signup and view all the answers

What is the name of the mathematician who is considered one of the greatest minds of all history?

<p>Archimedes (B)</p> Signup and view all the answers

What is the shape for which Archimedes calculated the surface area and volume?

<p>Sphere (D)</p> Signup and view all the answers

What is the name of the ancient Greek philosopher who is NOT associated with the development of mathematics?

<p>Aristotle (A)</p> Signup and view all the answers

What is the term used to describe the method of computing the area of a shape by inscribing and circumscribing polygons?

<p>Exhaustion method (A)</p> Signup and view all the answers

What is the name of the book that contains the content about Archimedes' life and contributions?

<p>History of Mathematics: Early Ages (D)</p> Signup and view all the answers

Where was Jamshid al-Kashi born?

<p>Kashan, in central Iran (B)</p> Signup and view all the answers

What was the name of the Zij produced by Al-Kashi?

<p>Khaqani Zij (C)</p> Signup and view all the answers

What was the basis of Al-Kashi's Zij, the Khaqani Zij?

<p>Nasir al-Din al-Tusi’s earlier Zij-i Ilkhani (D)</p> Signup and view all the answers

What was the resolution of sinus values calculated by Al-Kashi in his Zij?

<p>Each degree is divided into 60 minutes (C)</p> Signup and view all the answers

How many entries were there in Al-Kashi's sinus table in his Zij?

<p>5400 (B)</p> Signup and view all the answers

What was the precision of Al-Kashi's calculation of sinus values in his Zij?

<p>Up to 8th decimal (C)</p> Signup and view all the answers

How did Al-Kashi calculate the value of π?

<p>By inserting a polygon with 805,306,368 edges inside a circle (A)</p> Signup and view all the answers

How long did Al-Kashi's record of calculating π stand?

<p>200 years (B)</p> Signup and view all the answers

Who was the founder of an institute in Samarkand that became a prominent university?

<p>Ulugh Beg (A)</p> Signup and view all the answers

How many scientists were teaching and doing research at Ulugh Beg's institute in Samarkand?

<p>Around 60 (C)</p> Signup and view all the answers

Where did Ulugh Beg found an institute that became a prominent university?

<p>Samarkand (C)</p> Signup and view all the answers

What was the name of the Zij produced by Al-Kashi?

<p>Khaqani Zij (A)</p> Signup and view all the answers

What was the level of precision achieved by Al-Kashi in calculating sinus values in his Zij?

<p>Up to 8th decimal (C)</p> Signup and view all the answers

What was the purpose of Ulugh Beg's institute in Samarkand?

<p>To gather great mathematicians and scientists of the Middle East (A)</p> Signup and view all the answers

How did Al-Kashi calculate the value of π?

<p>By inserting a polygon with 805,306,368 edges inside a circle (D)</p> Signup and view all the answers

How long did Al-Kashi's record of calculating π stand?

<p>200 years (D)</p> Signup and view all the answers

What was the resolution of the sinus values calculated by Al-Kashi?

<p>Each degree divided into 60 minutes (C)</p> Signup and view all the answers

Who founded an institute in Samarkand that became a prominent university?

<p>Ulugh Beg (B)</p> Signup and view all the answers

What was the name of the city where Al-Kashi was born?

<p>Kashan, in central Iran (A)</p> Signup and view all the answers

How many entries were there in Al-Kashi's sinus table in his Zij?

<p>5400 entries (A)</p> Signup and view all the answers

What was the main purpose of Ulugh Beg's institute in Samarkand?

<p>To gather many great mathematicians and scientists (A)</p> Signup and view all the answers

What was the basis of Al-Kashi's Zij-i Ilkhani?

<p>Nasir al-Din al-Tusi's earlier Zij (B)</p> Signup and view all the answers

What was the name of the city where Al-Kashi worked?

<p>Samarkand (D)</p> Signup and view all the answers

What was the level of precision achieved by Al-Kashi in calculating π?

<p>Up to 16th decimal (B)</p> Signup and view all the answers

What was the resolution of sinus values calculated by Al-Kashi?

<p>1 minute (B)</p> Signup and view all the answers

What was the reason for the importance of Ulugh Beg's institute in Samarkand?

<p>It was a center of astronomy and mathematics (B)</p> Signup and view all the answers

How long did Al-Kashi's record of calculating π stand?

<p>200 years (C)</p> Signup and view all the answers

What was the name of the Zij produced by Al-Kashi?

<p>Khaqani Zij (A)</p> Signup and view all the answers

How many edges did Al-Kashi use to calculate π?

<p>805,306,368 (B)</p> Signup and view all the answers

What was the significance of Ulugh Beg's institute in Samarkand?

<p>It was a center of learning for students from all over the Middle East and beyond (A)</p> Signup and view all the answers

Flashcards

Exhaustion Method

A method of finding area by using inscribed and circumscribed polygons to approximate the shape.

Who was Archimedes?

A Greek mathematician, physicist, engineer, inventor, and astronomer, considered one of the greatest mathematicians in history.

Archimedes' Value of π

Ï€ is between 3 10/71 and 3 10/70

The Museum of Alexandria

An ancient library and museum in Alexandria.

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Modern integration

A calculation preformed by the method of exhaustion.

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Archimedes' Sphere Calculation

The surface area and volume of a sphere.

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Who was Jamshid al-Kashi?

A Persian astronomer and mathematician who produced very accurate astronomical tables.

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Khaqani Zij

An astronomical table ('Zij') created by Al-Kashi.

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Basis of Khaqani Zij

Nasir al-Din al-Tusi's earlier Zij-i Ilkhani

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Al-Kashi's Sinus Resolution

Each degree divided into 60 minutes.

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Al-Kashi's Sinus Table Entries

5400 entries.

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Al-Kashi's Sinus Precision

Up to the 8th decimal place.

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Al-Kashi's π Calculation

By inserting a polygon with 805,306,368 edges inside a circle.

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Al-Kashi's π Record

200 years.

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Founder of Samarkand Institute

Ulugh Beg founded it.

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Scientists at Ulugh Beg's institute

Around 60 scientists

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Location of Ulugh Beg's institute

Samarkand

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Al-Kashi's Sinus Precision

Up to the 8th decimal place

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Purpose of Ulugh Beg's institute

To gather great scientists

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Al-Kashi's birthplace

Kashan, in central Iran

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Al-Kashi's Sinus Table Entries

5400 entries.

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Main purpose of Ulugh Beg's institute

To gather many scientists

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Basis of Al-Kashi's Zij-i-Ilkhani

Nasir al-Din al-Tusi's earlier Zij

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Al-Kashi's work location

Samarkand

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Al-Kashi's π Precision

Up to 16th decimal

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Al-Kashi's Sinus Resolution

1 Minute

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Importance of Ulugh Beg's institute

Center of astronomy and math

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Al-Kashi's Edges

805,306,368

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Significance of Ulugh Beg's institute

Learning students from all over

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Al-Kashi's Zij

Khaqani Zij

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