Fibonacci sequence

Play around with the Fibonacci sequence and discover some surprising results!

Leonard writes down a sequence of numbers. Can you find a formula to predict the seventh number in his sequence?

Investigate Farey sequences of ratios of Fibonacci numbers.

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

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

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

Using only the red and white rods, how many different ways are there to make up the other rods?

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

What have Fibonacci numbers got to do with Pythagorean triples?

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