How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF.
Similarly the largest equilateral triangle which fits into a circle is LMN and PQR is an equilateral triangle with P and Q on the line LM and R on the circumference of the circle. Show that LM = 3PQ
Can you spot a cunning way to work out the missing length?
This resource has a few rough edges. It was used as a test bed in the development of other NRICH materials. You have been warned!
In Plex, you see a representation of the Complex Plane, also known as an Argand diagram.
Pressing the Edit button reveals a script that allows you to adjust what will be displayed
when you press Run. I'll explain the script and give other examples on the way.
I hope that explains the basics. Clicking on a variable will popup a box where you can adjust its definition, colour, and drawMode. You may define quite a few variables and explore the point geometry of the complex plane in some detail. Try adding a couple more points such as: u=w*i and v=u*i. Can you predict the result? What about w=sqrt(i)*z, v=sqrt(i)*w,... ?
Once you are confident with Plex, try Plex2.