Or search by topic
There are 16 NRICH Mathematical resources connected to Golden ratio, you may find related items under Fractions, decimals, percentages, ratio and proportion.Broad Topics > Fractions, decimals, percentages, ratio and proportion > Golden ratio
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.
Nick Lord says "This problem encapsulates for me the best features of the NRICH collection."
Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.
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.
Find the link between a sequence of continued fractions and the ratio of succesive Fibonacci numbers.
Leonardo who?! Well, Leonardo is better known as Fibonacci and this article will tell you some of fascinating things about his famous sequence.
When is a Fibonacci sequence also a geometric sequence? When the ratio of successive terms is the golden ratio!
Given a regular pentagon, can you find the distance between two non-adjacent vertices?
Solve an equation involving the Golden Ratio phi where the unknown occurs as a power of phi.
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?
The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.
You add 1 to the golden ratio to get its square. How do you find higher powers?
Explore the geometry of these dart and kite shapes!
Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.
Show that the arithmetic mean, geometric mean and harmonic mean of a and b can be the lengths of the sides of a right-angles triangle if and only if a = bx^3, where x is the Golden Ratio.
Without using a calculator, computer or tables find the exact values of cos36cos72 and also cos36 - cos72.