### Cellular

Cellular is an animation that helps you make geometric sequences composed of square cells.

### Geometric Parabola

Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.

### Summing Geometric Progressions

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

# Squaring the Circle and Circling the Square

##### Stage: 4 Challenge Level:
 Part 1 If you can see this message Flash may not be working in your browser Please see http://nrich.maths.org/techhelp/#flash to enable it. 1) What is the area of the red portion of this figure? Click NEXT 2) What is the area of the blue portion of this figure? Click NEXT 3) What is the area of the orange portion of this figure? If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
 Part 2 Now imagine that instead of the pattern growing, we start with a square and the pattern continues inwards - with the circles and squares becoming smaller and smaller. If the areas of the four blue shapes labelled A, B, C and D are one unit each, what is the combined area of all the blue shapes? Explain any reasoning you have used.