Other tags that relate to A Third of the Area
Ratio. Mathematical reasoning & proof. Similarity and congruence. Quadratic equations. 2D shapes and their properties. Pythagoras' theorem. Golden ratio. Angle properties of polygons. Interactivities. Creating and manipulating expressions and formulae.There are 7 results
Broad Topics > Fractions, Decimals, Percentages, Ratio and Proportion > Golden ratio
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.
Golden Thoughts
Age 14 to 16 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.
Pentakite
Age 14 to 18 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.
Leonardo of Pisa and the Golden Rectangle
Age 7 to 16
Leonardo who?! Well, Leonardo is better known as Fibonacci and this article will tell you some of fascinating things about his famous sequence.
Whirling Fibonacci Squares
Age 11 to 16
Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.
The Golden Ratio, Fibonacci Numbers and Continued Fractions.
Age 14 to 16
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.
NRICH is part of the family of activities in the Millennium Mathematics Project.