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Broad Topics >

Patterns, Sequences and Structure > Fibonacci sequence

##### 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.

##### Age 14 to 16 Challenge Level:

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

##### Age 11 to 16 Challenge Level:

Can you beat the computer in the challenging strategy game?

##### Age 7 to 16

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

##### Age 11 to 14 Challenge Level:

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?

##### 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.

##### Age 14 to 16

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.

##### Age 14 to 18

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

##### 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?

##### 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. . . .

##### Age 11 to 16 Challenge Level:

Using logo to investigate spirals

##### 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.

##### 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?

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 16

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

##### Age 7 to 14

Second of two articles about Fibonacci, written for students.

##### Age 14 to 16 Challenge Level:

Explore the transformations and comment on what you find.