MAT336: History of Mathematics

Spring 2026

Study Guide: Quiz 5

Plimpton 322 — Inca Mathematics — Maya Mathematics

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.

Part 1: Quiz-Style Questions

Plimpton 322

  1. What is Plimpton 322? Where was it found? When is it dated?
  2. Using the reciprocal pair method with r = 4/3 , generate a Pythagorean triple. Show all steps.
  3. Why must the parameter r in the reciprocal pair method be a regular number in base 60? State the precise computational reason and illustrate with an appropriate example.
  4. Describe a precise numerical relationship satisfied by the entries in the second and third columns of any row of Plimpton 322.
  5. Three interpretations of Plimpton 322 have been discussed in class. Name them and briefly describe each.
  6. Many scholars argue Plimpton 322 cannot be a trigonometric table. Give at least two of their reasons.
  7. Many scholars argue Plimpton 322 cannot be a table of Pythagorean triples. Give at least one of their reasons.
  8. Give two features of the tablet that suggest a school or teaching context.
  9. Show algebraically why the reciprocal pair method always produces a Pythagorean triple.
  10. A Babylonian triangle typically looks very different from the triangle most people draw today. Describe both and explain what this difference reveals about how mathematics is culturally shaped.
  11. Recall that when we solved in class the Old Babylonian problem “a number and its reciprocal differ by 7,” we saw that it leads to a quadratic equation. Using the interpretation of Plimpton 322 discussed in class, explain how each row of the tablet could be connected to the solution of such a problem.

Part 2: Reflection Questions

Plimpton 322

  1. We discussed in class that ancient mathematical texts must be understood in their historical context. What does this mean, and why does it matter for interpreting Plimpton 322?
  2. Robson writes: “Any resemblance Plimpton 322 might bear to modern mathematics is in our minds, not his.” Do you agree? Is it possible to fully escape our own mathematical framework when reading ancient texts?

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