Fibonacci sequence

problem

Pythagorean Fibs

Age

16 to 18

Challenge level

What have Fibonacci numbers got to do with Pythagorean triples?
problem

Sheep Talk

Age

7 to 11

Challenge level

In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?
problem

Golden Fractions

Age

16 to 18

Challenge level

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

Plus or Minus

Age

16 to 18

Challenge level

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

Room Doubling

Age

7 to 11

Challenge level

Investigate the different ways you could split up these rooms so that you have double the number.
article
Fibonacci's Three Wishes 2

Second of two articles about Fibonacci, written for students.
article
Leonardo of Pisa and the Golden Rectangle

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

Colour Building

Age

11 to 14

Challenge level

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

1 Step 2 Step

Age

11 to 14

Challenge level

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
problem
Favourite

Fibonacci Surprises

Age

11 to 14

Challenge level

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