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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.