Golden ratio

There are 16 NRICH Mathematical resources connected to Golden ratio

problem

Gold Again

Age

16 to 18

Challenge level

Without using a calculator, computer or tables find the exact values of cos36cos72 and also cos36 - cos72.

problem

Golden Thoughts

Age

14 to 16

Challenge level

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

article

Whirling Fibonacci Squares

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

article

The Golden Ratio, Fibonacci Numbers and Continued Fractions.

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.

article

Leonardo of Pisa and the Golden Rectangle

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

article

About Pythagorean Golden Means

What is the relationship between the arithmetic, geometric and harmonic means of two numbers, the sides of a right angled triangle and the Golden Ratio?

Or search by topic

Number and algebra

Geometry and measure

Probability and statistics

Working mathematically

Advanced mathematics

For younger learners

Golden ratio

Gold Again

Golden Thoughts

Whirling Fibonacci Squares

The Golden Ratio, Fibonacci Numbers and Continued Fractions.

Leonardo of Pisa and the Golden Rectangle

About Pythagorean Golden Means