Beautiful Examples of Mathematics in                              Nature

                                         

  1. Sunflowers

                                    

Bright, bold and beloved by bees, sunflowers boast radial symmetry and a type of numerical symmetry known as the Fibonacci sequence, which is a sequence where each number is determined by adding together the two numbers that preceded it. For example: 1, 2, 3, 5, 8, 13, 21, 24, 55, and so forth.

 2. Nautilus Shell

     

                                        

• A nautilus is a cephalopod mollusk with a spiral shell and numerous short tentacles around its mouth.
• Although more common in plants, some animals, like the nautilus, showcase Fibonacci numbers. A nautilus shell is grown in a Fibonacci spiral. The spiral occurs as the shell grows outwards and tries to maintain its proportional shape.

3. Romanesco Broccoli

  

Romanesco broccoli has an unusual appearance, and many assume it’s another food that’s fallen victim to genetic modification. However, it’s actually one of many instances of fractal symmetry in nature.n geometric terms, fractals are complex patterns where each individual component has the same pattern as the whole object. In the case of romanseco broccoli, each floret is a miniaturised version of the whole head’s logarithmic spiral. This means the entire veggie is one big spiral composed of smaller, cone-like mini-spirals.

4. Pinecones

                                        

Pinecones have seed pods that arrange in a spiral pattern. They consist of a pair of spirals, each one twisting upwards in opposing directions.

• The number of steps will almost always match a pair of consecutive Fibonacci numbers. For example, a three–to–five cone meets at the back after three steps along the left spiral and five steps along the right.

5. Honeycombs

                                               

• Honeycombs are an example of wallpaper symmetry. This is where a pattern is repeated until it covers a plane. Other examples include mosaics and tiled floors.
• Mathematicians believe bees build these hexagonal constructions because it is the shape most efficient for storing the largest possible amount of honey while using the least amount of wax. Shapes like circles would leave gaps between the cells because they don’t fit perfectly together.

6. Milky Way Galaxy

                                                                                                                                                                                 

Recently, a new section on the edges of the Milky Way Galaxy was discovered, and, by studying this, astronomers now believe the galaxy is a near-perfect mirror image of itself.

• Using this new information, scientists have become more confident in their theory that the galaxy has only two major arms: the Scutum-Centaurus and the Perseus.
• As well as having mirror symmetry, the Milky Way has another amazing design. Like nautilus shells and sunflowers, each ‘arm’ of the galaxy symbolises a logarithmic spiral that begins at the galaxy’s centre and expands outwards.
• 
  

7. Peacocks

                                

• Most animals have bilateral symmetry, which means drawing an even centre line would create two matching halves.
• The peacock takes the earlier principle of using symmetry to attract a mate to the nth degree. In fact, Charles Darwin, who famously conceived the survival of the fittest theory, detested peacocks. 
• Darwin thought the peacock’s tail was a burden that made no evolutionary sense. He remained furious until coming up with the theory of sexual selection, which asserts that animals develop certain features to increase their chances of mating. Male peacocks utilise their variety of adaptations to seduce sultry peahens. These include bright colours, a large size, a symmetrical body shape and repeated patterns in their feathers.

 8. Sun-Moon Symmetry

                              

                                         

• The sun has a diameter of 1.4 million kilometres, while his sister, the Moon, has a meagre diameter of 3,474 kilometres. With these figures, it seems near impossible that the moon can block the sun’s light and give us around five solar eclipses every two years.                                                          By sheer coincidence, the sun’s width is roughly four hundred times larger than that of the moon, while the sun is about four hundred times further away. The symmetry in this ratio causes the moon and sun to appear almost the same size when seen from Earth, and, therefore, it becomes possible for the moon to block the sun when the two align.
• Earth’s distance from the sun can increase during its orbit. If an eclipse occurs during this time, we see what’s known as an annular or ‘ring’ eclipse. This is because the sun isn’t completely hidden.
• Every one to two years, though, the sun and moon become perfectly aligned, and we can witness a rare event called a total solar eclipse. 
• Astronomers don’t know how common this symmetry is between other planets, suns, and moons, but theorise that it’s quite rare. Every year, though, our moon drifts roughly four centimetres further from Earth. This means that, billions of years ago, every solar eclipse would have been a total eclipse.
• If things continue as they are, total eclipses will eventually cease entirely – as will annular eclipses, assuming the planet lasts that long. With this in mind, it’s easy to conclude that we’re simply in the right place at the right time to witness this phenomenon. Some have theorised that this sun-moon symmetry is the special factor which makes life on Earth possible.

                                          

  9.  Starfish

                                          

• Starfish or sea stars belong to a phylum of marine creatures called echinoderm. Other notable echinoderm include sea urchins, brittle stars, sea cucumbers and sand dollars.
• The larvae of echinoderms have bilateral symmetry, meaning the organism’s left and ride side form a mirror image. However, during metamorphosis, this is replaced with a superficial radial symmetry, where the organism can be divided into similar halves by passing a plane at any angle along a central axis.
• Sea stars or starfish are invertebrates that typically have five or more ‘arms’. These radiate from an indistinct disk and form something known as pentaradial symmetry.
• Their evolutionary ancestors are believed to have had bilateral symmetry, and sea stars do exhibit some superficial remnant of this body structure.

                     


10.  Orb Web Spiders

                             

• There are approximately 5,000 types of orb web spiders. All of them create near-perfect circular webs that have near-equal-distanced radial supports coming out of the middle and a spiral that is woven to catch prey.
• It’s not clear why orb spiders are so geometrically inclined. Tests have shown that orbed webs are no better at catching prey than irregularly shaped webs.
• Some scientists theorise that orb webs are built for strength, with radial symmetry helping to evenly distribute the force of impact when a spider’s prey makes contact with the web. This would mean there’d be less rips in the thread.

  

Mathematics Laboratory

The mathematics laboratory is a place where anybody can experiment and explore patterns and ideas. It is a place where one can find a collection of games, puzzles, and other teaching and learning material. The materials are meant to be used both by the students on their own and with their teacher to explore the world of mathematics, to discover, to learn and to develop an interest in mathematics. The activities create interest among students or in anybody who wants to explore, and test some of their ideas, beliefs about mathematics.

The activities in the maths lab should be appealing to a wide range of people, of different ages and varying mathematical proficiency. While the initial appeal is broad-based, the level of engagement of different individuals may vary. The maths lab activities listed here have been done with students and teachers of different grade levels. The activities are intended to give children an experience of doing mathematics and not merely for the purpose of demonstration.

The maths lab provides an opportunity for the students to discover mathematics through doing. Many of the activities present a problem or a challenge, with the possibility of generating further challenges and problems. The activities help students to visualize, manipulate and reason. They provide opportunity to make conjectures and test them, and to generalize observed patterns. They create a context for students to attempt to prove their conjectures.

It is important to note that while in science experiments provide evidence for hypotheses or theories, this is not so in mathematics. Observed patterns can only suggest mathematical hypotheses and conjectures, not provide evidence to support them. Mathematical truths are accepted only on the basis of proofs, and not through experiment.

Mathematics laboratory is a place to enjoy mathematics through informal exploration. It is a place where anyone can generate problems and struggle to get a answer. It is a space to explore and design new mathematical activities. So, the maths lab should not be used to assess students’ knowledge of mathematics. Often mathematics lab takes students knowledge beyond the curriculum.

Mathematics laboratory is a self-explanatory lab with activities, in which students could come any time and engage in the work, continue working on the problems/tasks, and use teachers as and when they are stuck. In this way, the role of the teacher is not to teach how to progress in the activity but to facilitate inquiry with the mathematics in it. The facilitation could be done either by probing questions, giving an extra resource or asking to follow or discuss with peers.