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Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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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.

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Ladder and Cube

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

Circumference and Diameter

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

The formula which gives in terms of is $C= \pi \times d$ , so the graph of C versus d is a straight line which passes through the origin.

This problem is taken from the UKMT Mathematical Challenges.
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