What is Rotational Symmetry?

buttercup displaying rotational or radial symmetry — one semicircle repeated 4 times at a duplication angle of 72 degrees around the centre creates the shape of the buttercup petals

Thanks to an opportunity to collaborate with our friends in the Clonakilty Bike Festival, we are putting together an activity on ‘What is Rotational Symmetry?’.

Details on the geometry of the pentagonal rotations available at Rotational symmetry of the Pentagon

Repeated patterns around a fixed point.

Rotational Symmetry can involve any number of repeated elements. You see it many places but probably don’t realise it.

Using just two elements in rotation is the humble playing card. Turn it 180 degrees around the three red diamonds in the centre and it’s identical. (It’s worth noting here that this is not a reflection it’s a rotation about a fixed point with just two elements; the two Kings)

Any object that moves on wheels features rotational symmetry. Hense the Bicycle Festival.

Rotational symmetry can also be called ‘planar radial’. Meaning 2 dimensional radial.

rotational or planar radial symmetry in citrus fruit

When we cut through a citrus fruit it has segments that lie around a centre point, displaying an image of 2D radial or rotational symmetry. (The Geometry in Food post has lots more on seeing shapes in food)

Flower petals also. (many plants have arrangements of petals that correlate to Fibonacci numbers in nature which is also form of radial symmetry).

3D radial explosion

In 3 dimensions the radial symmetry is again centred around a point but comes out in every direction like an explosion.

Again it’s about training the eye to see it. Like with our other shape hunting. We see it all the time but barely notice the perfect geometry.

Most plants show us some form of radial symmetry. Plant roots and branches when sliced show radial symmetry. Ever tried counting the rings in a tree?

Radial Symmetry organisms

Some marine creatures also have this radial like symmetry. Think of anemones, sea urchins, corals and starfish.

shells showing rotational or radial symmetry

So many things have this type of radial symmetry in them , once you start looking you be amazed how many you see, remember the star in the apple?

Cycle Festival Event

On June 8th 2014 The Smart Happy Project hosted a 5K cycle ride in conjunction with the Clonakilty Bicycle Festival. A family event, we hunted for nature and rotational symmetry. Photos are on the Events page.

pattern showing planar radial or rotational symmetry on a watering can

To see an example of an similar activity looking for shapes in nature have a look at the scavenger hunt clues post.

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Thanks

Lisa

What is Rotational Symmetry?