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The Best Square

How would you judge a competition to draw a freehand square?


Explore the properties of combinations of trig functions in this open investigation.

A Different Differential Equation

Explore the properties of this different sort of differential equation.

Chance of That

Age 16 to 18
Challenge Level

This is an open investigation. It can be taken to various levels of complexity and note that the construction of non-trivial examples is, in itself, difficult.


I was looking at two seemingly random lists of 12 whole numbers chosen from 1 to 5. The sample correlation was exactly zero.
Convince yourself that such a list of numbers is possible. Can you get a feel for the properties of such lists?
Explore the properties and frequencies of such lists of numbers, perhaps varying the two numbers involved.
For more investigations see our Stage 5 pages.