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?

  • π ∈ [3 10/71, 3 10/70] (correct)
  • π ∈ [3 1/4, 3 1/3]
  • 3.14
  • π ∈ [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</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</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</p> Signup and view all the answers

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

    <p>Sphere</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</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</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</p> Signup and view all the answers

    Where was Jamshid al-Kashi born?

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

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

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

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

    <p>5400</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</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</p> Signup and view all the answers

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

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

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

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

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

    <p>Samarkand</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

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

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

    <p>Samarkand</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</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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