Limits

problem
Favourite

Spokes

Age

16 to 18

Challenge level

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.
problem

Resistance

Age

16 to 18

Challenge level

Find the equation from which to calculate the resistance of an infinite network of resistances.
problem

Triangle Incircle Iteration

Age

14 to 16

Challenge level

Keep constructing triangles in the incircle of the previous triangle. What happens?
article
Fractional Calculus I

You can differentiate and integrate n times but what if n is not a whole number? This generalisation of calculus was introduced and discussed on askNRICH by some school students.
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Fractional Calculus II

Here explore some ideas of how the definitions and methods of calculus change if you integrate or differentiate n times when n is not a whole number.
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Fractional Calculus III

Fractional calculus is a generalisation of ordinary calculus where you can differentiate n times when n is not a whole number.
problem
Favourite

Witch of Agnesi

Age

16 to 18

Challenge level

Sketch the members of the family of graphs given by $y = a^3/(x^2+a^2)$ for $a=1, 2$ and $3$.
problem
Favourite

Converging Product

Age

16 to 18

Challenge level

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)... ?
problem
Favourite

Rain or Shine

Age

16 to 18

Challenge level

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.
problem

Over the Pole

Age

16 to 18

Challenge level

Two places are diametrically opposite each other on the same line of latitude. Compare the distances between them travelling along the line of latitude and travelling over the nearest pole.