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

Ruler

Age

16 to 18

Challenge level

The interval 0 - 1 is marked into halves, quarters, eighths ... etc. Vertical lines are drawn at these points, heights depending on positions. What happens as this process goes on indefinitely?
problem

A Swiss Sum

Age

16 to 18

Challenge level

Can you use the given image to say something about the sum of an infinite series?
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?
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.
article
Continued Fractions I

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