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Contemplative Mathematics: Leading Math Discussion Groups

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  1. Introduction

    Introduction to Socratic Mathematics (Preview Content)
    2 Topics
    |
    1 Quiz
  2. Sessions
    Session 1: Figurate Numbers
    2 Topics
    |
    1 Quiz
  3. Session 2: Square Numbers
    2 Topics
    |
    1 Quiz
  4. Session 3: Co-primality
    3 Topics
    |
    1 Quiz
  5. Session 4: Co-primality and Fractions
    2 Topics
    |
    1 Quiz
  6. Session 5: A Numerical Puzzle
    2 Topics
    |
    1 Quiz
  7. Session 6: Another Numerical Puzzle
    2 Topics
    |
    1 Quiz
  8. Session 7: The Bridges of Köningsberg
    2 Topics
    |
    1 Quiz
  9. Session 8: Patterns in Graphs
    2 Topics
    |
    1 Quiz
  10. Session 9: Chromatic Graphs
    2 Topics
    |
    1 Quiz
  11. Conclusion
    Concluding Remarks
    1 Topic
  12. End of Course Test
    End of Course Test: Contemplative Mathematics
    1 Quiz
Lesson Progress
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  • What is the next (i.e. the fifth) square number?
  • Why is it easier to find the 113th square number than the 113th triangular number? How would you find the 113th square number?
  • What is the nth square number? Easier or harder than for triangular numbers?
  • Let’s say that I tell you the 202nd square number. It’s 40,804. Could you find out the 203rd square number in an easy way? Maybe even in your head? (This is also secretly a question about generalization: how do you go from the nth square number to the (n+1)th? Why does that work?
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