Which Twin Is Older?

A simplified account of special relativity and the twins paradox.

Snookered

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

Spokes

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

A Rational Search

Stage: 4 and 5 Challenge Level:

Note that this open investigation can be taken to many levels of complexity.

A large circle of unit radius is constructed. From this initial circle, the following diagram is constructed using only straight edges and compasses :

All circles touch or intersect at tangents only. The initial circle has an area of $\pi$ units squared - this is an irrational area.

Hidden in the image is at least one region with a rational area. Can you find one?

This image could be extended in many ways. How many regions of rational area could you construct using only straight edge and compasses? What interesting images can you construct? What questions do these generate in your mind?

For more investigations see our Stage 5 pages.