Using three parameters a, b and c, mark each arrow with an operation and parameter, e.g. +a or /c.[br][br][[b][size=85]You can see a numerical example by going [url=https://ggbm.at/hdddfgqq]here[/url].[/size][/b] [b][size=85]If you [u][i]are[/i][/u] using numerical values for the parameters, do not use +0 or -0 or x1 or /1[/size][/b]. [color=#ff0000][i][b]Certainly do not use /0[/b][/i].[color=#000000]][/color][br][/color][br]No two arrows may be marked with the same operation and parameter.[br][br]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.[br][br]Can you devise way(s) to concatenate these sequences to produce a one dimensional periodic lattice of numbers?[br][br]Can you devise way(s) to concatenate these sequences to produce a two dimensional periodic lattice of numbers?[br][br]Can you devise way(s) to concatenate these sequences to produce a three dimensional periodic lattice of numbers?[br][br][color=#ff0000][i][b]What questions could / would you put to your students based on this applet?[/b][/i][/color]