Golden ratio

problem

Darts and Kites

Age

14 to 16

Challenge level

Explore the geometry of these dart and kite shapes!
problem

Golden Triangle

Age

16 to 18

Challenge level

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.
problem

Golden Powers

Age

16 to 18

Challenge level

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

Pent

Age

14 to 18

Challenge level

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.
problem

Golden Fibs

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!
problem

Golden Fractions

Age

16 to 18

Challenge level

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

Gold yet Again

Age

16 to 18

Challenge level

Nick Lord says "This problem encapsulates for me the best features of the NRICH collection."
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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
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.