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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.
Explore the properties of this iterative geometrical procedure
Investigate constructible images which contain rational areas.
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
How would you judge a competition to draw a freehand square?
What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?
Explore the properties of this different sort of differential equation.
Explore the properties of combinations of trig functions in this open investigation.
What can you create using 140 characters and our cool Twilgo environment?
Explore creating 'factors and multiples' graphs such that no lines joining the numbers cross
If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?
In the limit you get the sum of an infinite geometric series. What about an infinite product (1+x)(1+x^2)(1+x^4)... ?
Find the shape and symmetries of the two pieces of this cut cube.