Introducing a geometrical instrument with 3 basic capabilities.
A task which depends on members of the group working
collaboratively to reach a single goal.
This task depends on groups working collaboratively, discussing and
reasoning to agree a final product.
Zebras are recognized by the black and white stripes they have all over their body. This (two-dimensional) pattern is unique and distinctive for each zebra, and it helps the animal in several situations in the wild.
First of all, it enables it to hide from one of its main predators, the lion. The vertical stripes camouflage the zebra when it hides in tall grass, and the colour-blind lions cannot spot it! Moreover, a herd of zebras moving together, might appear as one large animal, with the individual zebras being indistinguishable - hence predators will find it hard to isolate
one and hunt it. The stripes have been formed on zebras as a natural consequence of evolution and adaptation to the environment.
2. Plagiomnium Affine
A very typical example of a plant cellular structure, we see how cells are arranged in two dimensions, forming a tissue. In this particular tissue, we observe that the plant cells are hexagonal in shape.
The plant cells are of fixed shape because they are held together by the rigid cellular wall in their exterior. The cellular wall is of great importance in plants (as well as other species which have the structure) because it protects the interior of the cell, it prevents over-expansion when water enters the cell, and it maintains a rigid shape for the cell.
Also note the many chloroplasts which are visible in these cells, the organelles which conduct photosynthesis for the plant.
Hemoglobin is a protein found in the red blood cells, and it acts as an oxygen transporter. It consists of four polypeptide chain subunits, and so it obtains the so-called quaternary structure. In our picture, those chains are the $\alpha$ (alpha) subunit, in red, and the $\beta$ (beta) subunit in blue (and this type of Hemoglobin is called A Hemoglobin,
and is the most common form in humans). The green structures are the heme groups, and they mostly consist of iron. Their main purpose is to have the oxygen attached to them for transportation.
4. Gephyrocapsa Oceanica
The Gephyrocapsa Oceanica is a type of algae. The pattern to observe here is called the coccolith. It consists of calcium carbonate plates, which are formed by single - celled algae called coccolithopores. Then, the plates form this spherical structure which we observe in the picture, and which is called a coccosphere. The reason why this pattern
forms is still unknown, but a few hypotheses have been made. So, perhaps the coccoliths are formed in order for the algae to be protected by zooplankton or bacteria, or perhaps they are formed to increase buoyancy, or to release carbon dioxide for photosynthesis, or to filter harmful UV light.
A honeycomb consists of a two - dimensional pattern, in which many hexagonal wax cells are built next to each other. The honey bees build the honeycombs in order to store their honey and pollen, and also to protect their larvae.
There are two interesting theories about the hexagonal shape of the honeycomb. The first is supported by the fact that hexagonal tiles cover a given volume of space with a lattice of minimal surface area. Thus, the bees use the least material and energy in order to create their home.
The second theory claims that the honeycombs take this very neat pattern because all the bees form it simultaneously together. As evidence to support the theory, one might observe that the queen bee cells are completely irregular.
A pinecone is a pattern in three dimensions. Its name is inspired by the fact that it resembles more or less a cone in three dimensions (though sometimes the tip of the pinecone might be wide and its base narrow, so that it resembles more a cylinder).
A tree normally has both male and female pinecones. The male pinecone is very similar amongst almost all types of conifer trees, and is herbaceous. The female pinecone, on the other hand, has a big variety and is normally used to identify the type of each conifer tree. The familiar "woody" pinecone is female, like the one depicted in this photograph.
The female cone produces the seeds used to reproduce the plant. The scales observed are supposed to open when the ovules are produced in order to be fertilized by the male pollen, then to close so that the seeds are protected when developping, and then open again in order for the mature seeds to escape and form a new plant.
Therefore, the pattern we observe in pinecones serves the function of reproduction for the plant.
7. Erythrocytes (Red blood cells)
In this picture we observe a somewhat random arrangement of red blood cells. In general, red blood cells do not form particular patterns in three dimensions, precisely because the blood is fluid, and so its components flow freely.
Their shape, however, has an interesting structure, being a disc which is flattened in the centre. This is called a biconcave disc shape, and it is very useful for the flow of blood inside the arteries and veins. The red colour of the cells is because of their high content in hemoglobin, which is the protein responsible for oxygen transfer.
In snails, we observe a very interesting two-dimensional spiral shape in their shells. The shells are used as a means of protection by snails, both against predators and against natural conditions (e.g. the sun or drying-out). Moreover, it serves as an exosceleton for the snail, so that its muscles are attached there.
9. Intestine villi
This picture shows a pattern in two dimensions, depicting the villi of a human's intestine. The villi are long projections from the intestinal wall, whose main function is to absorb the nutrients from the various foods that circulate there. This shape of the intestinal wall considerably increases the surface area from which the human can absorb the nutrients, and
also makes the process much more efficient, since the diffusion of the nutrients can only happen in a very small distance.
Clearly this is one of the most interesting patterns in human biology. The famous three-dimensional model of the DNA, consisting of a double helix of polenucleotide chains has uncovered many of the features of the human genes.
One of the most important structural features of the DNA is the fact that the bases are paired, in the sense that Adenine is only connected to Thymine and vice versa, and Guanine is only connected to Cytosine and vice versa. This helps us understand how the copying of the DNA works, which is important for the preservation of the genetical information of the cell.
Moreover, this feature also helps us understand how the DNA transcription works, which explains the synthesis of proteins.
The property of the DNA to spiral itself also helps it shrink to a very small volume, compared to its length. In fact, the DNA in a single human cell is estimated to have a length of 2 meters. This shows how the genetic information can be stored safely and still be expressed.