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. . . .
Leonardo who?! Well, Leonardo is better known as Fibonacci and this article will tell you some of fascinating things about his famous sequence.
These gnomons appear to have more than a passing connection with the Fibonacci sequence. This problem ask you to investigate some of these connections.
How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?
Can you beat the computer in the challenging strategy game?
Here are some circle bugs to try to replicate with some elegant programming, plus some sequences generated elegantly in LOGO.
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!
An article introducing continued fractions with some simple puzzles for the reader.
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.
Using logo to investigate spirals
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?
Cellular is an animation that helps you make geometric sequences composed of square cells.
This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.
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.
Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.
Explore the transformations and comment on what you find.