SPIRALS

Spirals are curved lines that rotate around a centre and they move further away from it at each turn.

The separation between each turn is constant.

The separation between each turn increases in a certain way.

The separation between each turn depends on the sequence of numbers 1, 1, 2, 3, 5, 8, 13...

This is known as the Fibonacci sequence.

To look like the shape of the Archimedean spiral, the spirals can be constructed with two or more centres using a ruler and a compass. If a spiral has more centres, the separation between the turns will be closer to a constant value.

Some examples of spirals are:

Construct a spiral with two centres

To construct a spiral given the two points A and B, follow these steps:

Step 1. Draw the segment AB.

Step 2. Use centre point A and radius AB. Draw half a circumference from B to C.

Step 3. Use centre point B and radius BC. Draw half a circumference from C to D.

Step 4. Use centre point A and radius AD. Draw half a circumference from D to E.

Step 5. Use centre point B and radius BE. Draw half a circumference from E to F, forming a spiral from the segment AB.

Construct a spiral with three centres

To construct a spiral with three centres, A, B and C, follow these steps:

Step 1. Draw an equilateral triangle ABC.

Step 2. Extend the sides of the triangle.

Step 3. Use centre point A and radius AC.

Draw an arc from C to D.

Step 4. Use centre point B and radius BD.

Draw an arc from D to E.

Step 5. Use centre point C and radius CE.

Draw an arc from E to F, forming a spiral with three centres.