A voyage of discovery through a sequence of challenges exploring properties of the Golden Ratio and Fibonacci numbers.

What have Fibonacci numbers to do with solutions of the quadratic equation x^2 - x - 1 = 0 ?

What have Fibonacci numbers got to do with Pythagorean triples?

Investigate Farey sequences of ratios of Fibonacci numbers.

Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.

When is a Fibonacci sequence also a geometric sequence? When the ratio of successive terms is the golden ratio!

Leonardo who?! Well, Leonardo is better known as Fibonacci and this article will tell you some of fascinating things about his famous sequence.

A first trail through the mysterious world of the Golden Section.

These gnomons appear to have more than a passing connection with the Fibonacci sequence. This problem ask you to investigate some of these connections.

You add 1 to the golden ratio to get its square. How do you find higher powers?

Here are some circle bugs to try to replicate with some elegant programming, plus some sequences generated elegantly in LOGO.

Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.

Let a(n) be the number of ways of expressing the integer n as an ordered sum of 1's and 2's. Let b(n) be the number of ways of expressing n as an ordered sum of integers greater than 1. (i) Calculate. . . .

Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.

Can you beat the computer in the challenging strategy game?

This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.

An article introducing continued fractions with some simple puzzles for the reader.

Find the link between a sequence of continued fractions and the ratio of succesive Fibonacci numbers.

For which values of n is the Fibonacci number fn even? Which Fibonnaci numbers are divisible by 3?

Cellular is an animation that helps you make geometric sequences composed of square cells.

An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.

Investigations and activities for you to enjoy on pattern in nature.