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Resources tagged with Golden ratio similar to Sierpinski Triangle:

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

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Golden Triangle

Stage: 5 Challenge Level: Challenge Level:1

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.

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Golden Fibs

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

When is a Fibonacci sequence also a geometric sequence? When the ratio of successive terms is the golden ratio!

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Pentabuild

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Pent

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Golden Ratio

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Golden Powers

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Gold Again

Stage: 5 Challenge Level: Challenge Level:1

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

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Golden Eggs

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Golden Construction

Stage: 5 Challenge Level: Challenge Level:1

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

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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.

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Golden Thoughts

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Golden Mathematics

Stage: 5

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

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Whirling Fibonacci Squares

Stage: 3 and 4

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

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Golden Fractions

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Pythagorean Golden Means

Stage: 5 Challenge Level: Challenge Level:1

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.

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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.

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Darts and Kites

Stage: 4 Challenge Level: Challenge Level:1

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.

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Golden Trail 1

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

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

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About Pythagorean Golden Means

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?

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Gold Yet Again

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Pentakite

Stage: 4 and 5 Challenge Level: Challenge Level:1

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.