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Resources tagged with Fibonacci sequence similar to Gold Again:

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Broad Topics > Sequences, Functions and Graphs > Fibonacci sequence

Leonardo of Pisa and the Golden Rectangle

Stage: 2, 3 and 4

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

Golden Mathematics

Stage: 5

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

Golden Powers

Stage: 5 Challenge Level:

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

Golden Fractions

Stage: 5 Challenge Level:

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

Golden Fibs

Stage: 5 Challenge Level:

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

Pythagorean Fibs

Stage: 5 Challenge Level:

What have Fibonacci numbers got to do with Pythagorean triples?

Farey Fibonacci

Stage: 5 Short Challenge Level:

Investigate Farey sequences of ratios of Fibonacci numbers.

Continued Fractions I

Stage: 4 and 5

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

Whirling Fibonacci Squares

Stage: 3 and 4

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

Gnomon Dimensions

Stage: 4 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.

Fibonacci Fashion

Stage: 5 Challenge Level:

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

LOGO Challenge - Circles as Bugs

Stage: 3 and 4 Challenge Level:

Here are some circle bugs to try to replicate with some elegant programming, plus some sequences generated elegantly in LOGO.

Stage: 3 and 4 Challenge Level:

Using logo to investigate spirals

Plus or Minus

Stage: 5 Challenge Level:

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

Got a Strategy for Last Biscuit?

Stage: 3 and 4 Challenge Level:

Can you beat the computer in the challenging strategy game?

The Golden Ratio, Fibonacci Numbers and Continued Fractions.

Stage: 4

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.

Stringing it Out

Stage: 4 Challenge Level:

Explore the transformations and comment on what you find.

Building Gnomons

Stage: 4 Challenge Level:

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

Cellular

Stage: 2, 3 and 4 Challenge Level:

Cellular is an animation that helps you make geometric sequences composed of square cells.

First Forward Into Logo 11: Sequences

Stage: 3, 4 and 5 Challenge Level:

This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.

Ordered Sums

Stage: 4 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. . . .

Fibonacci Factors

Stage: 5 Challenge Level:

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