MAT336: History of Mathematics

Spring 2026

Study Guide: Quiz 10 Lecture 1

India

Note: This is a study guide. The quiz will consist of three or four questions covering the material below. If you understand the ideas and facts in the non-computational questions and can work through the computational problems, you will be well prepared.

Note on review questions: This quiz will also include one or two questions drawn from earlier in the course (Quizzes 1–3). The review questions are listed at the end of this study guide.

Part 1: India

  1. Place the following in rough chronological order, giving approximate centuries and a one-sentence description of each: the Indus/Harappan civilization, the Śulba Sūtras, Aryabhata, the Bakhshali manuscript, and the Gwalior temple inscription.
  2. Give a one-sentence description of the Indus (Harappan) civilization. Then state two pieces of archaeological evidence that support your description of it as an organized urban civilization.
  3. Why are the Śulba Sūtras historically important for mathematics, and what kind of mathematical presentation do they use?
  4. State, in words and in the style of the Śulba Sūtras, the rule about the diagonal of a square. Then restate it in precise modern mathematical language.
  5. State, in words and in the style of the Śulba Sūtras, the rule about the diagonal of a rectangle. Then restate it in precise modern mathematical language.
  6. In Aryabhata's system for encoding numbers, consonants represent digits and vowels represent place values. Explain in one or two sentences why this system presupposes place value. Does Aryabhata need to write a zero symbol in order to use place value?
  7. Give a two-sentence description of Aryabhata's system for encoding numbers, and explain why it was useful for transmitting mathematical and astronomical information.
  8. What is a radian? Give a definition in your own words.
  9. Indian astronomers used a circle of radius R = 3438. Explain where this number comes from.
  10. Greek astronomers tabulated chords; Indian mathematicians worked with half-chords (jya). What is the geometric relationship between a chord and the corresponding jya? Why is the jya easier to work with?
  11. What is the Bakhshali manuscript? Give its approximate date according to the most recent Oxford radiocarbon dating. Why is it important in the history of mathematics? Give two reasons.
  12. What is the difference between zero as a placeholder and zero as a number? Give one example of each.
  13. The Gwalior temple inscription is sometimes described as the oldest definitively dated zero in India. What is its date, and what number does it record? What makes it significant?

Part 2: Review Questions

Quiz 1 — Sources and Counting

  1. If you found a 9th-century Arabic translation of Apollonius’s Conics (written in 3rd century BCE), would this be a primary source for studying: (a) Apollonius’s mathematical ideas? (b) 9th-century Arabic translation practices? Explain your reasoning.
  2. Is the following statement true or false? “There is scholarly consensus that the Ishango bone represents a base-10 counting system.” Explain your answer.
  3. Define primary source and secondary source. What is the key difference between them?

Quiz 2 — Number Systems

  1. What is the difference between a numeral and a number?
  2. What makes a number system positional?
  3. Why do positional systems need zero?

Quiz 3 — Ancient Egypt

  1. Using the method of false position: A quantity and its 1/7 added together become 19. Find the quantity.
  2. Judging from the Rhind and Moscow papyri, how was mathematics learned and transmitted in Ancient Egypt?
  3. What is the Rhind Mathematical Papyrus? In which century was it written, and what was its purpose?

Quiz Problem Rubric

Points Criteria
3 Correct answer with reasoning/work shown
2 Partially correct with some reasoning shown
1 Correct answer without reasoning/work OR significant attempt with some understanding
0 Incorrect or blank

Notes