What pattern do you see? Would you get the "same" pattern with the repeating decimal 0.231231...?
Build patterns for these numbers: (a) 0.2222... (b) 0.121212... (c) 0.12341234... (d) 0.1234512345... (e) 0.102102... (For digit 0, make a 90^{o} turn, but move no distance)...What do you notice?

Try 7ths: 1/7 = 0.142857...; 2/7 = 0.285714...; etc. What geometric principles are in play?

What does it take for a repeating decimal to have a closed path--one where the repeated digits will repeat a particular path?

What would you expect to happen with the digit patterns for the numbers π or e? Why?

Could a repeating decimal create a line segment that keeps increasing in discrete jumps?

What decimal would create the diagram shown above?

Now, make up your own questions for exploration....

**Note:** These explorations are part of the idea of Spirolaterals.

Source: From a conference workshop given by Bob Kansky (WY), a good and respected friend.

**Hint:** No hint needed...just start exploring....

**Solution Commentary:** No solution commentary needed...as the patterns and exploration guidelines are in front of you.