Limits of sequences

problem
Archimedes and numerical roots

Age

14 to 16

Challenge level

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
problem
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
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
Climbing powers

Age

16 to 18

Challenge level

Does it make any difference how we write powers of powers?
article
Infinite continued fractions

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

In this article we show that every whole number can be written as a continued fraction of the form k/(1+k/(1+k/...)).
article
Continued fractions I

An article introducing continued fractions with some simple puzzles for the reader.
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?