# Algebraic Tessellations

- Author:
- Judah L Schwartz

- Topic:
- Algebra

Using three parameters a, b and c, mark each arrow with an operation and parameter, e.g. +a or /c.
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**You can see a numerical example by going here.****If you**.__using numerical values for the parameters, do not use +0 or -0 or x1 or /1__*are**.] No two arrows may be marked with the same operation and parameter. Construct two different sequences of operations and parameters that each transform any given number through a series of intermediate steps and that ultimately return the original number. Can you devise way(s) to concatenate these sequences to produce a one dimensional periodic lattice of numbers? Can you devise way(s) to concatenate these sequences to produce a two dimensional periodic lattice of numbers? Can you devise way(s) to concatenate these sequences to produce a three dimensional periodic lattice of numbers?***Certainly do not use /0****What questions could / would you put to your students based on this applet?**