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Resources tagged with Fibonacci sequence similar to Pythagorean Fibs:

Other tags that relate to Pythagorean Fibs

Powers & roots. Pythagorean triples. Surds. Golden ratio. Generalising. Interactivities. Mathematical reasoning & proof. Fibonacci sequence. Quadratic equations. Making and proving conjectures.

There are 24 results

Broad Topics > Sequences, Functions and Graphs > Fibonacci sequence

Pythagorean Fibs

Stage: 5 Challenge Level:

What have Fibonacci numbers got to do with Pythagorean triples?

Fibonacci Fashion

Stage: 5 Challenge Level:

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

Golden Mathematics

Stage: 5

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

Plus or Minus

Stage: 5 Challenge Level:

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

Farey Fibonacci

Stage: 5 Short Challenge Level:

Investigate Farey sequences of ratios of Fibonacci numbers.

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 Fibs

Stage: 5 Challenge Level:

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

Fibonacci Factors

Stage: 5 Challenge Level:

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

Golden Trail 1

Stage: 3, 4 and 5 Challenge Level:

A first trail through the mysterious world of the Golden Section.

Golden Powers

Stage: 5 Challenge Level:

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

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.

Golden Fractions

Stage: 5 Challenge Level:

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

Continued Fractions I

Stage: 4 and 5

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

Got a Strategy for Last Biscuit?

Stage: 3 and 4 Challenge Level:

Can you beat the computer in the challenging strategy game?

Whirling Fibonacci Squares

Stage: 3 and 4

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

Building Gnomons

Stage: 4 Challenge Level:

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

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.

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.

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.

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. . . .

Magical Maze - 35 Activities

Stage: 4 and 5

Investigations and activities for you to enjoy on pattern in nature.

Stringing it Out

Stage: 4 Challenge Level:

Explore the transformations and comment on what you find.