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. . . .
These gnomons appear to have more than a passing connection with
the Fibonacci sequence. This problem ask you to investigate some of
Investigations and activities for you to enjoy on pattern in
A first trail through the mysterious world of the Golden Section.
An article introducing continued fractions with some simple puzzles for the reader.
Build gnomons that are related to the Fibonacci sequence and try to
explain why this is possible.
Play around with the Fibonacci sequence and discover some surprising results!
Leonardo who?! Well, Leonardo is better known as Fibonacci and this article will tell you some of fascinating things about his famous sequence.
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.
Can you beat the computer in the challenging strategy game?
Second of two articles about Fibonacci, written for students.
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?
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.
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?
Using logo to investigate spirals
This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.
Cellular is an animation that helps you make geometric sequences composed of square cells.
Explore the transformations and comment on what you find.