Mathematics is everywhere. We are often unaware of it but, when we observe our environment consciously, we can see mathematical structures all around us.

This footbridge is a cornucopia of mathematical forms.

Recently, while waiting for a train in Blackrock Station (Co Dublin), I photographed various objects in and around the station. There were circles and squares all about, parallel planes and lines, hexagons and helices.

The footbridge crossing the railway line was a particularly rich source of mathematical images. Some of the photographs appear below. They are just a small sample of the wealth of mathematical images and concepts that are in evidence here and, indeed, everywhere.

We enter the station portico between two columns, the Ionic capitals ornamented by volutes. The floor is covered by a regular pattern of square tiles. The station sign and the advertisement case on the right are rectangular in form and there are many rectangles in the door-frame. So, immediately, we can see cylinders, spirals, squares and rectangles.

Passing through the rectangular door to the platform, we see the footbridge (pictured above). At the back of the platforms are railings, providing fields of parallel lines:

Zooming further in, each bar of the railing is a rough cylinder. Behind the railings the distinct horizontal line of the horizon is clear:

The platform of the footbridge is a beautiful prismatic volume, hexagonal in cross-section. Although not a regular hexagon (with all sides and angles equal), it has opposite sides parallel:

There is a variety of polygonal forms, with rhombi (fence), squares (floor), hexagons (nuts) and octagons (lamp-post):

Plane surfaces are evident in the glass and concrete structures, with vertical and horizontal planes intersecting in lines:

Looking closely at the bolts securing the footbridge we find helical grooves. The helix is one of the simplest truly three-dimensional curves:

Finally, circular forms are in abundance in many of the structures:

These mathematical forms were easy to find in a quick scan over a few minutes before the arrival of the train. We have not even mentioned converging rail-tracks and hanging catenaries, or the waves on the sea surface or ripples in the sand. A more exhaustive search would certainly yield many further riches. There is nothing unique about Blackrock station. Mathematical forms are to be found everywhere.

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