Math Problem Statement

Answer

There are 13 left-handed and 21 right-handed spirals on the cacti in the photograph. What is special about these numbers?

Solution

The numbers 13 and 21 are both part of the Fibonacci sequence, where each term is the sum of the two preceding ones. The sequence starts like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on.

In the context of the question:

  • 13 and 21 are consecutive Fibonacci numbers (13 being the 7th term and 21 being the 8th term).
  • This is significant because many natural phenomena, including the arrangement of spirals in plants (like the spirals on the cactus shown), often follow the Fibonacci sequence.

Hence, the correct answer is:

A. They are consecutive terms in the Fibonacci sequence.

Would you like more details or have any questions?

Here are five related questions for further exploration:

  1. How is the Fibonacci sequence related to the golden ratio?
  2. Can you explain why the Fibonacci sequence appears in nature?
  3. What is the next Fibonacci number after 21?
  4. How can you calculate Fibonacci numbers without a calculator?
  5. Are there any other sequences that commonly appear in nature?

Tip: The Fibonacci sequence is closely related to the golden ratio, as the ratio of consecutive Fibonacci numbers approximates this special number, 1.618...

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Math Problem Analysis

Mathematical Concepts

Fibonacci Sequence
Natural Patterns

Formulas

Fibonacci Sequence: F(n) = F(n-1) + F(n-2)

Theorems

Fibonacci Theorem
Golden Ratio

Suitable Grade Level

Grades 7-10