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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.

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?

# Estimating Time

#### How well can you estimate time?

Start by trying to estimate exactly ten seconds:

Full Screen and tablet version

You could have several attempts and then analyse the data from the table. You could collect data from several people to do some interesting comparisons.

Here are some questions you might like to consider:

Are people better at estimating short amounts of time (10 or 15 seconds) or longer time intervals (30 or 60 seconds)?

If a person's first attempt is an over-estimate, do they tend to underestimate on their second go?

If you are better than your partner at estimating 10 seconds, are you more likely to also be better at estimating longer time intervals?

Are older people better at estimating than younger people?

Do people get better at estimating if they practise?

Some people estimate time by reciting or singing something of a specific length, others by counting, others by visualising the hands of a clock...
Which strategies for estimating are most effective?

Is a person who is better at estimating time also likely to be better at estimating angles? Try Estimating Angles.

Does someone who can react faster also judge time intervals better? Try Reaction Timer