Fibonacci sequence

problem
Favourite

Fibs

Age

11 to 14

Challenge level

The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?
article
Whirling Fibonacci Squares

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

Logo Challenge - Circles as Bugs

Age

11 to 16

Challenge level

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

First Forward Into Logo 11: Sequences

Age

11 to 18

Challenge level

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

Last Biscuit

Age

11 to 18

Challenge level

Can you find a strategy that ensures you get to take the last biscuit in this game?
article
The Golden Ratio, Fibonacci Numbers and Continued Fractions

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.
problem

Building Gnomons

Age

14 to 16

Challenge level

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

Gnomon Dimensions

Age

14 to 16

Challenge level

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

Ordered Sums

Age

14 to 16

Challenge level

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 a(n) and b(n) for n<8. What do you notice about these sequences? (ii) Find a relation between a(p) and b(q). (iii) Prove your conjectures.
article
Continued Fractions I

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