### There are 21 results

Broad Topics >

Patterns, Sequences and Structure > Fibonacci sequence

##### Age 16 to 18 Challenge Level:

Find the link between a sequence of continued fractions and the
ratio of succesive Fibonacci numbers.

##### Age 16 to 18 Challenge Level:

You add 1 to the golden ratio to get its square. How do you find higher powers?

##### Age 11 to 16

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

##### Age 16 to 18

A voyage of discovery through a sequence of challenges exploring
properties of the Golden Ratio and Fibonacci numbers.

##### 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 14 to 18

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

##### Age 16 to 18 Challenge Level:

Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.

##### Age 16 to 18 Challenge Level:

What have Fibonacci numbers got to do with Pythagorean triples?

##### Age 16 to 18 Challenge Level:

When is a Fibonacci sequence also a geometric sequence? When the
ratio of successive terms is the golden ratio!

##### Age 16 to 18 Challenge Level:

What have Fibonacci numbers to do with solutions of the quadratic
equation x^2 - x - 1 = 0 ?

##### 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 11 to 16 Challenge Level:

Can you beat the computer in the challenging strategy game?

##### 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 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 16 to 18 Short Challenge Level:

Investigate Farey sequences of ratios of Fibonacci 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 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 14 to 16 Challenge Level:

Explore the transformations and comment on what you find.

##### Age 16 to 18 Challenge Level:

For which values of n is the Fibonacci number fn even? Which
Fibonnaci numbers are divisible by 3?

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

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