Discuss the following questions with your classmates. Each question is followed by a hint — try to reason it out before reading the hint.

1.     A whole sheet of paper is folded in half again and again. Each fold doubles the number of layers. Why might the number of layers become impossible to fold after only seven or eight folds, even though the rule sounds so simple?

Hint: Think about the doubling pattern you studied in this chapter, and how quickly it grows compared to how slowly the number of folds increases.

2.     Rangoli designs are often built with a repeating pattern around a central point. Why do you think symmetry and repetition make a design look pleasing, rather than a design where every part is different?

Hint: Consider how easy or difficult it is for your eyes and brain to “predict” what the rest of a symmetric design will look like.

3.     Why do you think the same Virahanka pattern that was discovered by studying Sanskrit poetry also appears in the number of petals on many flowers and in the golden-ratio spirals of shells?

Hint: Patterns are not owned by any one subject. The same rule can describe very different things — sound, shape, and growth — if the underlying logic is the same.

4.     If you were only given the terms 2, 4, 8 and asked to find the next term, could the rule definitely be “double it”, or could there be another rule that also fits these three terms?

Hint: Try to think of at least one other rule, different from doubling, that would also produce 2, 4, and 8 as its first three terms.

5.     A computer that recognises handwritten numbers is trained by looking at thousands of examples of handwriting. How is this similar to the way you found the rule for the triangular or square numbers in this chapter?

Hint: Think about the Observe, Identify, Predict, Verify process, and which of these steps a computer might also need to follow.

Last modified: Thursday, 8 October 2026, 7:31 AM