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Resources tagged with Golden ratio similar to Golden Powers:

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Broad Topics > Fractions, Decimals, Percentages, Ratio and Proportion > Golden ratio

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!

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 Trail 1

Stage: 3, 4 and 5 Challenge Level:

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

Golden Mathematics

Stage: 5

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

Whirling Fibonacci Squares

Stage: 3 and 4

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

Pentakite

Stage: 4 and 5 Challenge Level:

ABCDE is a regular pentagon of side length one unit. BC produced meets ED produced at F. Show that triangle CDF is congruent to triangle EDB. Find the length of BE.

Golden Triangle

Stage: 5 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.

Gold Again

Stage: 5 Challenge Level:

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

Gold Yet Again

Stage: 5 Challenge Level:

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

Golden Thoughts

Stage: 4 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.

Golden Ratio

Stage: 5 Challenge Level:

Solve an equation involving the Golden Ratio phi where the unknown occurs as a power of phi.

Pentabuild

Stage: 5 Challenge Level:

Explain how to construct a regular pentagon accurately using a straight edge and compass.

Darts and Kites

Stage: 4 Challenge Level:

A rhombus PQRS has an angle of 72 degrees. OQ = OR = OS = 1 unit. Find all the angles, show that POR is a straight line and that the side of the rhombus is equal to the Golden Ratio.

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.

Golden Construction

Stage: 5 Challenge Level:

Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.

Pent

Stage: 4 and 5 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.

Golden Eggs

Stage: 5 Challenge Level:

Find a connection between the shape of a special ellipse and an infinite string of nested square roots.