Problem 102 - College Algebra

Question

Enough curiosities involving the Fibonacci sequence exist to warrant a flourishing Fibonacci Association, which publishes a quarterly journal. Do some research on the Fibonacci sequence by consulting the Internet or the research department of your library, and find one property that interests you. After doing this research, get together with your group to share these intriguing properties.

Step-by-Step Solution

Answer

The Fibonacci sequence is a series of numbers where each number is the sum of the two numbers before it. One interesting property found during the research is the 'Golden Ratio', where the ratio between two consecutive Fibonacci numbers approaches approximately 1.618 as the numbers increase in the sequence.

Step 1: Understanding the Fibonacci sequence

First, it's crucial to understand what the Fibonacci sequence is. This sequence is an ordering of numbers where each number is the sum of the two preceding ones. It often starts with 0 and 1.

Step 2: Researching the Fibonacci sequence

Once the basic concept of the Fibonacci sequence is understood, research this sequence on various sources like internet, books, or by consulting the research department of your library.

Step 3: Choosing an interesting property

After doing the research, pick one property that you find particularly fascinating. For instance, the 'Golden Ratio' property is an interesting one: As the Fibonacci numbers increase, the ratio between two consecutive numbers approaches the Golden Ratio, which is approximately 1.618.