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'Making Spirals' printed from https://nrich.maths.org/
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There are lots of different spirals and lots of different ways of creating them.
One way of making a spiral is by following the instructions to make Archimedes' Spiral.
Another type of spiral is a Golden (or Fibonacci) Spiral.
Can you see how this one has been made?
When you've looked carefully at the picture and thought about this, have a look at the instructions for making a Golden Spiral:
Take a piece of A4 squared or graph paper. The best one to use is one that is divided into 5mm squares. Put the paper down so that its longest side is horizontal.
Start by drawing a square with a side of one about 10 squares up from the bottom edge of the paper and 15 squares in from the right hand side.
Draw another square with a side of one above it.
Now draw a square of side two to the right of your first two squares and then a square of side 3 above that.
You can now start to draw your spiral.
Each square has a quarter of a circle in it which joins one corner of the square to its opposite corner.
Can you see where to draw your next square and curve?
The sizes of your squares follow the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34. Can you see why? You will run out of space on your paper when you get to 21 or 34 - it depends on exactly where you positioned your first square on the paper.
Start by drawing a square with a side of one about 10 squares up from the bottom edge of the paper and 15 squares in from the right hand side.
Draw another square with a side of one above it.
Now draw a square of side two to the right of your first two squares and then a square of side 3 above that.
You can now start to draw your spiral.
Each square has a quarter of a circle in it which joins one corner of the square to its opposite corner.
Can you see where to draw your next square and curve?
The sizes of your squares follow the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34. Can you see why? You will run out of space on your paper when you get to 21 or 34 - it depends on exactly where you positioned your first square on the paper.
What do you notice about these spirals? Are they similar?
Can you create any more rules for making your own spirals?