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
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/...)).
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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
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
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
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?