Nature, education and geometry

As we all know, geometry is around us, however, not always our students are aware of this fact. For this reason, today I have some examples that show how close we are to geometry and also how to take advantage of it in our lessons.

The first example I want to share with you is the famous Giant’s Causeway. 

Let’s see first some details

It is an area that is compounded by 40 000 basalt columns, it was created because of an eruption of a volcano 60 million years ago. It is located in Northern Ireland and it was declared a World Heritage site in 1986.

The history of this area is based on a myth. It is said that many years ago, two giants, one from Ireland and the other from Staffa had a bad relationship and they were constantly throwing rocks at each other. After throwing all those rocks they created a long field of rocks.

The Scottish giant decided to walk the path of rocks and defeat his enemy. When the wife of the other giant saw the Scottish giant coming, she decided to dress up her husband as a baby. When the Scottish giant saw the size of this baby got scared and ran away sinking all the rock into the water so his enemy could not get him. 

Have a look at this video: https://www.youtube.com/watch?v=4gcYu3gIANM

Why do I consider this as an attractive resource for students?

First of all, because the story of this place is based on a myth that might catch their attention. Then I consider that if we want to introduce geometric aspects to our students, we should do it in a way in which they could see how this theme is connected with real life and not just in their textbooks. 

As we can see in these photos, this field of rocks is made of 40.000 hexagons which are regular polygons. Showing real examples can help our students to remember things easily since they have learnt them in a funny and interesting way. 

Which kind of activity could we do? 

Show this picture to your students and ask them to identify which geometry elements they can find. Then invite them to recreate those figures with paper and create in class your own field of rocks. Maybe if you consider it appropriate ask them to create other regular polygons so you can reinforce their previous knowledge. 

The second example of geometry in nature is the hives.

We are very close to bees, maybe because we are afraid of them or just because we like them. However, you might not realise their way of eating as well as the way they collect their food. It is not that simple because these little insects have created the greatest resource to keep their food safe and also to be able to keep a huge number of them. Can you guess how they did it? Yes, again we see how geometry has influenced their mechanisms. 

Let’s see some background 

The first mathematician that was interested in this topic was Pappus of Alejandría ( around the year 320 of our era). He had his “ Mathematic collections”, book V, in which he worked with Isoperimetric inequality, which means the comparison of areas and volumes of figures with the same perimeter or area. For example, he was trying to come up with different geometric figures that contained the biggest volume on the same surface. Therefore, here is the first example of the investigation of hives.

 

Nevertheless, he was not the only mathematician that was interested in this topic, indeed, Kepler was fond of the shape of the hives. Not only because of its hexagonal structure but also for what was inside the cell too, he used to call them “quilla”. 

He describes them like this:

Each cell is surrounded by the other six, they are separated by the adjacent in common. If you observe what it is inside each cell we will realise that it is inclined at an obtuse angle made by three planes. In this way, they can keep a huge amount of honey.

Interesting website: 

http://www.matematicasvisuales.com/html/geometria/rhombicdodecahedron/honeycomb.html

Possible activity: 

With foam rubber, you can create different hexagons and construct with the students your own hive. As you can put these hexagons together or separate them, take advantage of it and let students manipulate them. You could work with the angles and also you can create different structures from those hexagons.  

Finally, we have our third example: 

Our final example is the famous spider web. All the construction of this spider web has to do with geometry, let’s see an example:

The centre in which the spider resides is the barycentre of the triangle structure, the point at which the three medians are cut. The barycentre has the ability to be the gravity centre on the triangle. The spider situated its own weight and also of her/his prey in this point so the stability is guaranteed.

There are other spider webs that do not have a triangle shape, however, they still have this gravity point.  

The real construction of a spider web: https://www.youtube.com/watch?v=N6C4zu1dF7A

Why did the spider choose this shape?

Because the triangle has a non-deformable characteristic and also it provides enough resistance.

Activity:

Make a circle with your students and with a ball, create your own spider web. The student will be able to see clearly the triangles and they will have fun while doing this activity that not only works geometry but also psychomotricity skills.

                                                                       References

El panal de las abejas. (2020). Matemáticas visuales. http://www.matematicasvisuales.com/html/geometria/rhombicdodecahedron/honeycomb.html

Luján, A. (2018, 17 agosto). National Geographic. www.nationalgeographic.com.es. https://www.nationalgeographic.com.es/fotografia/foto-del-dia/calzada-gigantes_12948

Sorando, J. M. (2019). Geometría de una telaraña- Matemáticas en tu mundo. Matemáticas en tu mundo. http://matematicasentumundo.es/NATURALEZA/naturaleza_telarana.htm