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. . . .
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?
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.
These gnomons appear to have more than a passing connection with
the Fibonacci sequence. This problem ask you to investigate some of
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.
Build gnomons that are related to the Fibonacci sequence and try to
explain why this is possible.
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?
Second of two articles about Fibonacci, written for students.
An article introducing continued fractions with some simple puzzles for the reader.
This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.
Can you beat the computer in the challenging strategy game?
Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.
Using logo to investigate spirals
Here are some circle bugs to try to replicate with some elegant
programming, plus some sequences generated elegantly in LOGO.
Cellular is an animation that helps you make geometric sequences
composed of square cells.
Investigations and activities for you to enjoy on pattern in
Explore the transformations and comment on what you find.