Fancy something very substantial? These challenging investigations will take time and you will need to pose your own questions in order to make your own mathematical discoveries.

problem

### Trig-trig

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

problem

### Chance of that

What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?

problem

### A different differential equation

Explore the properties of this different sort of differential
equation.

problem

### Investigating Twilgo

What can you create using 140 characters and our cool Twilgo environment?

problem

### Factors and multiples graphs

Explore creating 'factors and multiples' graphs such that no lines joining the numbers cross

problem

### Few and far between?

Can you find some Pythagorean Triples where the two smaller numbers differ by 1?