### Surds

Find the exact values of x, y and a satisfying the following system of equations: 1/(a+1) = a - 1 x + y = 2a x = ay

### The Root of the Problem

Find the sum of the series.

### Fit for Photocopying

Photocopiers can reduce from A3 to A4 without distorting the image. Explore the relationships between different paper sizes that make this possible.

# Origami Shapes

##### Stage: 4 Challenge Level:

The first thing to notice when solving this problem is that the sides of a sheet of A4 paper are in the ratio $1$ to $\sqrt{2}$ . (Check this by taking a sheet and measuring it.)

It simplifies the working a great deal if we treat the sheet of A4 paper as a rectangle with sides $1$ and $\sqrt{2}$, and keep the working exact by leaving the square roots in our expressions rather than typing them into a calculator.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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