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Resources tagged with Golden ratio similar to Agile Algebra:

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

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.

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 Fractions

Stage: 5 Challenge Level:

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

Golden Ratio

Stage: 5 Challenge Level:

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

Golden Mathematics

Stage: 5

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

Golden Powers

Stage: 5 Challenge Level:

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

Gold Again

Stage: 5 Challenge Level:

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

Golden Eggs

Stage: 5 Challenge Level:

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

Whirling Fibonacci Squares

Stage: 3 and 4

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

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.

Pentabuild

Stage: 5 Challenge Level:

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

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.

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!

Stage: 5

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?

Darts and Kites

Stage: 4 Challenge Level:

Explore the geometry of these dart and kite shapes!

Pythagorean Golden Means

Stage: 5 Challenge Level:

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.

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.

Gold Yet Again

Stage: 5 Challenge Level:

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

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.

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.