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Steve Phelps, 2017. 7. 1.

GeoGebra Global Gathering 2017 [math]Next = \frac{Now + 1}{Last}[/math]: From Elementary Mathematics to Cubic Curves with GeoGebra Steve Phelps GeoGebra Institute of Ohio (USA) Madeira High School University of Cincinnati Email: steve.phelps@geogebra.org Twitter: @giohio This is a presentation for the 2017 GeoGebra Global Gathering, which chronicles my GeoGebra investigation into a simple little problem found in these two resources: [list] [*]Sawyer, W.W. (1961). Lyness’ Periodic Sequence. The Mathematical Gazette, Vol. 45, No. 353, p. 207. The Mathematical Association of America [*]Lyness, R.C. (1961). Cycles. The Mathematical Gazette, Vol. 45, No. 353, p. 207-209. The Mathematical Association of America [/list] The problem is so simple, it can be readily understood by an elementary school student, yet is deep and rich enough to be the focus of graduate level mathematics research.


  • 1. Lyness' Periodic Sequence
  • 2. The Original Problem
  • 3. CAS the Lyness Sequence
  • 4. The Art of Problem Posing
  • 5. What-If-Not: The Original Problem
  • 6. The Original Problem in 2D
  • 7. What-If-Not: The Original Problem in 2D
  • 8. The Steps of the Sequence and Invariant Curve
  • 9. What-If-Not: Complex Number Lyness Sequence
  • 10. Functions in a Lyness Sequence
  • 11. Simple Lyness Cubic

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Lyness' Periodic Sequence

– Steve Phelps

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