Limits of sequences

article
Zooming in on the Squares

Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
article
Infinite Continued Fractions

In this article we are going to look at infinite continued fractions - continued fractions that do not terminate.
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Small Steps

Age

16 to 18

Challenge level

Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.
problem
Favourite

Slide

Age

16 to 18

Challenge level

This function involves absolute values. To find the slope on the slide use different equations to define the function in different parts of its domain.
problem

How Does Your Function Grow?

Age

16 to 18

Challenge level

Compares the size of functions f(n) for large values of n.
problem

Little and Large

Age

16 to 18

Challenge level

A point moves around inside a rectangle. What are the least and the greatest values of the sum of the squares of the distances from the vertices?
problem
Favourite

Approximating Pi

Age

14 to 18

Challenge level

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?
problem
Favourite

Squareness

Age

16 to 18

Challenge level

The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?
problem

Light Blue - Dark Blue

Age

7 to 11

Challenge level

Investigate the successive areas of light blue in these diagrams.
problem
Favourite

Diminishing Returns

Age

11 to 14

Challenge level

How much of the square is coloured blue? How will the pattern continue?