Study Guide: Renaissance Mathematics and Review
Note: This is a study guide. The quiz will consist of three or four questions covering the material below. If you understand the ideas in the conceptual questions and can work through the computations, you will be well prepared.
Part 1: Renaissance Mathematics
- Before the printing press, mathematical knowledge spread through hand-copied manuscripts. Describe two concrete consequences this had for how mathematics developed — and how printing changed them.
- Give one cause of mathematical change in the Renaissance and explain the specific mechanism of change.
- Why do Renaissance paintings often look more three-dimensional than medieval paintings? Give one mathematical reason.
- Why were algorithms with Hindu-Arabic numerals more efficient than those with Roman numerals? Give one reason connected to calculation, and one reason the system faced resistance in Europe.
- What was François Viète’s main contribution to algebraic notation? Explain the difference between solving one numerical problem and writing a general relation.
- What is a depressed cubic, and how was it used in solving cubic equations?
- Renaissance mathematicians treated x³ + ax = b and x³ = b + ax as different equations requiring separate methods. Why?
- When solving x³ = 15x + 4, Cardano’s formula involves √(−121) even though x = 4 is real. What was Bombelli’s contribution and why was it important for mathematics?
Quiz Problem Rubric
| Points | Criteria |
|---|---|
| 3 | Correct answer with reasoning or work shown |
| 2 | Partially correct with some reasoning shown |
| 1 | Correct answer without reasoning, or a significant attempt showing some understanding |
| 0 | Incorrect or blank |
Notes
- For computational problems: “reasoning/work” means steps shown.
- For conceptual problems: “reasoning” means explanation given.
- Round partial credit up when in doubt.