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Contemplative Mathematics: Leading Math Discussion Groups
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Introduction
Introduction to Socratic Mathematics (Preview Content)2 Topics|1 Quiz -
SessionsSession 1: Figurate Numbers2 Topics|1 Quiz
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Session 2: Square Numbers2 Topics|1 Quiz
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Session 3: Co-primality3 Topics|1 Quiz
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Session 4: Co-primality and Fractions2 Topics|1 Quiz
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Session 5: A Numerical Puzzle2 Topics|1 Quiz
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Session 6: Another Numerical Puzzle2 Topics|1 Quiz
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Session 7: The Bridges of Köningsberg2 Topics|1 Quiz
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Session 8: Patterns in Graphs2 Topics|1 Quiz
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Session 9: Chromatic Graphs2 Topics|1 Quiz
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ConclusionConcluding Remarks1 Topic
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End of Course TestEnd of Course Test: Contemplative Mathematics1 Quiz
Lesson 4,
Topic 3
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Discussion Questions
Lesson Progress
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- First Discussion: Collectively try to write out a rule that sorts pairs of numbers into coprime and not co-prime. Don’t feel obliged to use “mathematical” language: your goal is clarity and understanding. Conjecture boldly! Refine them in charity. Once you’ve come to consensus about your rule, you can play with it!
- Now that you have a conjectured rule everyone is happy with, try to break it! Propose pairs of numbers and see whether they fit the definition well.
- Can you make your rule shorter while saying the same thing?
- How does your rule categorize 0.4 and 1.2?
- Second Discussion: It’s always fun to compare our conjectures and ideas with mathematicians of yore. We participate in a great conversation across the millennia. You can play with Euclid’s definition of co-primality:
- Euclid VII, Def. 12: Numbers co-prime are those which are measured by a unit alone as a common measure.
- Does this say the same thing as your rule? Does it say it better? Worse? What are the trade-offs? What words in Euclid’s definition would you want to understand more?
