7414
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2011-02-01T00:00:01
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<ul id="stemLinks">
<li><a href="http://nrich.maths.org/5352">Warm-up</a></li>
<li><a href="http://nrich.maths.org/7668">Try this next</a></li>
<li><a href="http://nrich.maths.org/6155">Think higher</a></li>
<li><a href="http://nrich.maths.org/1322">Read: mathematics</a></li>
<li><a href="http://en.wikipedia.org/wiki/Symmetry_in_biology">Read: science</a></li>
<li><a href="http://plus.maths.org/content/os/issue30/features/dartnell/index">Explore further</a></li>
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<p>Mathematics is everywhere if you look carefully enough. Look at these 16 images. How many can you identify? What mathematics can you see in the images? Can you think of a reason for the shapes existing as they do? Can you spot shapes which share any common mathematical structures?<br></br>
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<div><mdo:image alt="" src="Poster.png" style="width: 600px; height: 534px;"></mdo:image></div>
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<div>Why not create your own poster of images from nature which exhibit mathematical structure, along with description, notes and explanations for the reader?</div>
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<div style="font-style: italic;">Note: these images are all in the public domain and taken from wikipedia commons.</div>
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<h3>Why do this problem?</h3>
<div><a href="https://nrich.maths.org/7414">This problem</a> is useful for opening students' minds to the links that exist between science and mathematics.</div>
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<div>Note that several of these images are also found on our <a href="http://nrich.maths.org/6308&part=">Scientific Measurement</a> problems, which will allow students to measure and estimate various physical attributes of the images.</div>
<h3>Possible approach</h3>
<div>This problem will very likely lead to interesting and rich discussion from the prompts in the question. </div>
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<div>As you lead the task it is important to be aware that there is no 'right' or 'complete' answers to any of these parts. Clearly, no teacher will be an expert in all of the underlying mathematics and science, so it is very acceptable to say 'I don't know' in response to questions. You might find that some students in the class emerge as experts in various areas of interest. All these students
to share their knowledge with the class. The teacher's role in this class is as a skilled facilitator: you want to help students to feel comfortable with sharing their ideas and exploring the links which emerge between mathematics and science.</div>
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<div>To help you to guide the discussion, we have included descriptions of the images (counting across from top left) along with some points of notes. These are not in any way an exhaustive list!</div>
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<h3>Key questions</h3>
<div>Zebra: Why black and White? Why stripes?</div>
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<div>Chloroplast (plant cell under magnification): What shapes form the structure? Why? (hexagons tesselate)</div>
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<div>Honeycomb: What shapes form the structure? Why? (hexagons tesselate; compare with choloplast).</div>
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<div>Pinecombs: These can be approximated as a cone, but also exhibit spiral structure.</div>
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<div>Representation of a protein: Proteins are very long and narrow and fold up into tight 'blobs' to preserve space. The way proteins fold is subject to intense mathematical analysis and requires the use of very powerful computers.</div>
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<div>Coccolith (single-celled organisms making up chalk): This shape is approximately spherical but the circles overlap in a way which is closely approximated by a dodecahedron.</div>
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<div>Snail: Snails have shells which grow in a 3D-spiral pattern</div>
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<div>Plant cells (from a beech tree): Similar to the chloroplast. Note the irregularities which have emerged from the straight hexagonal packing.</div>
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<div>Diatom (An alga under magnification): This is based on a regular octagon. Note that the angles are not exactly 45 degrees; this might be because the image is a 2D snapshot of a real 3D object; each of the legs is a cell. (see http://en.wikipedia.org/wiki/Asterionella for more detailed information_)</div>
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<div>Fin whale from the air: Note the the cross-section of this whale has an axis of symmetry and can be closely approximate by a kite. </div>
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<div>Pollen: The pollen particle shows amazingly beautiful mathematical structure, based an a C-60 buckyball.</div>
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<div>Vetruvian man: Leonardo Da Vinci sketched this image and points to the fact that the proportions of man are related to the Golden Ration.</div>
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<div>Snowflake: Snowflakes grow as accumulations of ice crystals; on a very fine scale they are hexagonal in structure.</div>
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<div>DNA (unravelled): DNA is usually tightly wound together similar to proteins. This DNA has been unravalled and we can see that it is long and very thin. As it fold up knots and complicated 'topologies' can occur.</div>
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<h3>Possible extension</h3>
<div>A lovely extension task is to get students to create their own posters of 16 mathematical images from natures, along with an accompanying description of the images, what mathematics underlies the images and what natural purpose the mathematical structure serves.</div>
<h3>Possible support</h3>
<div>Don't worry too much about the names of the objects and why they take these shapes: look for the mathematics and symmetries in the images.</div>
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<mdoxml version="1.0"><p style="text-align: justify;">We begin by identifying these pictures. From left to right and from top to bottom, they are:</p>
<p style="text-align: justify;"><strong>1.</strong> Zebra <strong>2.</strong> Plagiomnium Affine (plant cells) <strong>3.</strong> Honeycomb <strong>4.</strong> Pinecone</p>
<p style="text-align: justify;"><strong>5.</strong> Hemoglobine <strong>6.</strong> Gephyrocapsa Oceanica (coccolith) <strong>7.</strong> The Earth <strong>8.</strong> Snail</p>
<p style="text-align: justify;"><strong>9.</strong> <strong>10.</strong> Asterionella Formosa <strong>11.</strong> Whale <strong>12.</strong> Diatom</p>
<p style="text-align: justify;"><strong>13.</strong> Pollen <strong>14.</strong> Homo vitruvius <strong>15.</strong> Snowflake <strong>16.</strong> DNA</p>
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<p style="text-align: justify;">The first thing to identify in these pictures is <strong>symmetry</strong>. Almost all pictures have at least one axis of symmetry. In particular, we note the perfect symmetry of the Asterionella Formosa, with 4 axis of symmetry along its body, the detailed symmetry of the snowflake, which represents one of the most beautiful structures ever observed, and the
symmetry of the Homo Vitruvius, designed by Leonardo Da Vinci to emphasize on the beauty of the human form.</p>
<p style="text-align: justify;">Another mathematical aspect which we can identify are <strong>repeating patterns</strong>. Of particular interest are the plant cells and the honeycomb, both of which consist of many tiles of hexagons - a shape which considerably helps them carry out their biological functions more easily. We also note the repetitions in the pinecone, whose scales first close to
protect the fertilized seeds and afterwards open (a stage that we see now) in order for the seeds to spread.</p>
<p style="text-align: justify;"><strong>Curves</strong> also appear in some of these pictures. We note for example the spiral in the snail's shell, which helps it grow and protect itself. The DNA also takes various curved forms in order to fit into the small nucleous of the cell.</p>
<p style="text-align: justify;"><strong>Spherical structures</strong> are also very important in nature. From objects as small as the hemoglobine, a protein found in the red blood cells which helps the transportation of the oxygen, to objects as large as the Earth, many objects have a spherical form. We also observe a spherical Pollen, and a spherical Coccolith, a shape which mostly helps
these species protect themselves from their environment.</p>
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Maths is everywhere!
Maths is everywhere in the world! Take a look at these images. What mathematics can you see?
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