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Golden Thoughts
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.
At a Glance
The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
Contact
A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?
Age 14 to 16 Short
Challenge Level
A male punky fish has 9 stripes and a female punky fish has 8 stripes.
I count 86 stripes on the fish in my tank.
What is the ratio of male fish to female fish?
If you liked this question, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.