Geometrically an octagon is a polygon that has eight sides. 

A regular octagon is a closed figure with sides of the same length and internal angles of the same size. It has eight lines of reflective symmetry and rotational symmetry of order 8. The internal angle at each vertex of a regular octagon is 135°and the sum of all the internal angles of any octagon is 1080° (as with all polygons, the external angles total 360°).

The octagonal shape is used as a design element in architecture. The Dome of the Rock has a characteristic octagonal plan.

Umbrellas often have an octagonal outline.

Don’t you just love it when something comes together? When the timing of two things is just right; when two sounds coincide; when two people do something at just the same time.

The number 8 elicits words such as octave, octagon and octal. Eighth in Latin isoctavus. The perfect octave describes the interval between two pitches – one at one frequency and the other at half or double it’s frequency. This relationship has been described as the, ‘basic miracle of music’ and it is used extensively in most musical systems.

When I studied electronics I learned about frequencies. You start with one base frequency, but it’s very rare to find something that emits a single, pure frequency. Most musical instruments give out additional frequencies, which are called harmonics. They may be for, example, twice, three times, or half the base frequency. If you plot these together they are known as a harmonic series. The perfect octave is described in the harmonic series as the interval between the base harmonic and the second (twice the base) harmonic.

In sounds, the perfect octave sounds just right. I’ve started to study the piano and quickly saw that going from C to C produced a pleasing sound. I’ve played the guitar for many years and realised that the twelfth fret marks the second harmonic of the open strings.

The other harmonics that are generated can be a welcome sound or a great nuisance. They are what give a particular instrument it’s distinctive sound – the base note plus the additional harmonics. However, in radio and other systems electronics engineers spend a lot of time designing filters to prevent these harmonics from leaking out to the wider world as noise and power.

Is it fair too romantic to think of the perfect octave in terms of two people arriving at the same place at the same time? Is that what love at first sight looks and feels like? To be true to the analogy, a romantic arrival at a train station would have one person on one floor and the other on the next floor up – together, but apart.

Next time something comes together at just the right time, enjoy it for what it is.