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Dynamic Visual Models: Ancient Ideas and New Technologies

  • Damir Jungić
  • Veselin JungićEmail author
Conference paper
  • 30 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 313)

Abstract

We provide dynamic visual models of the following facts established by ancient mathematicians:
  1. 1.

    \(\sum _{i=1}^n(2i-1)=n^2\), \(n\in \mathbb {N}\),

     
  2. 2.

    \(\sum _{i=1}^ni=\frac{n(n+1)}{2}\), \(n\in \mathbb {N}\),

     
  3. 3.

    \(\sum _{i=1}^ni^2=\frac{n(n+1)(2n+1)}{6}\), \(n\in \mathbb {N}\),

     
  4. 4.

    \(\sum _{i=1}^ni^3=\left( \frac{n(n+1)}{2}\right) ^2\), \(n\in \mathbb {N}\).

     

We contrast the clarity of the models by outlining formal mathematical proofs based on those timeless ideas. We also reflect about the place that proofs play in the calculus classroom.

Keywords

Visual models Mathematical proof Teaching calculus 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada

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