![Geometric sequence
Bacteria such as Shewanella oneidensis multiply by doubling their
population in size after as little as 40 minutes. A geometric sequencesuch
as this, whereeach number is double the previous number [or f(n+1)
=2f(n)] produces a rapid increasein the population in a very shorttime.](https://image.slidesharecdn.com/b3dc9b40-62da-43bf-a952-f27f062f509a-151117134623-lva1-app6891/85/MATH-ONLINE-ASSIGNMENT-7-320.jpg)
MATH ONLINE ASSIGNMENT
- 1. Submitted to:Jaseena teacher Submitted by:Fathima Shahnaz
- 2. INTRODUCTION "The laws of nature are but the mathematical thoughts of God" - Euclid Mathematics is everywhere in this universe. Mathematics is all around us. As we discover more and more about our environment and our surroundings we see that nature can be described mathematically. The beauty of a flower, the majesty of a tree, even the rocks upon which we walk can exhibit natures sense of symmetry ,we seldom note it. We enjoy nature and are not interested in going deep about what mathematical idea is in it. Here are a very few properties of mathematics that are depicted in nature.
- 3. Symmetry Many mathematical principles are based on ideals, and apply to an abstract, perfect world. This perfect world of mathematics is reflected in the imperfect physicalworld, such as in the approximate symmetry of a face divided by an axis along the nose. More symmetricalfaces are generally regarded as more aesthetically pleasing. Five axes of symmetry are traced on the petals of this flower,fromeach dark purple line on the petal to an imaginary line bisecting the angle between the opposIng purplelines. The lines also trace the shapeof a star. Shapes - Perfect Earth is the perfect shape for minimising the pull of gravity on its outer edges - a sphere (although centrifugal force from its spin actually makes it an oblate spheroid, flattened at top and bottom). Geometry is the branch of maths that describes such shapes
- 4. Shapes - Polyhedra For a beehive, close packing is important to maximise the use of space. Hexagons fit most closely together without any gaps; so hexagonal wax cells are what bees create to storetheir eggs and larvae. Hexagons are six- sided polygons, closed, 2-dimensional, many-sided figures with straight edges. Geometry - Human induced People impose their own geometry on the land, dividing a random environmentinto squares, rectangles and bisected rhomboids, and impinging on the natural diversity of the environment.
- 5. Pi Any circle, even the disc of the Sun as viewed from Cappadoccia, central Turkey during the 2006 total eclipse, holds that perfect relationship where the circumferencedivided by the diameter equals pi. Firstdevised (inaccurately) by the Egyptians and Babylonians, the infinite decimal places of pi (approximately 3.1415926...) havebeen calculated to billions of decimal places. Fractals Many natural objects, such as froston the branches of a tree, show the relationship wheresimilarity holds at smaller and smaller scales. This fractal nature mimics mathematical fractalshapes where formis repeated at every scale. Fractals, such as the famous Mandelbrot set, cannotbe represented by. classical geometry Fibonacci sequence Rabbits, rabbits, rabbits. Leonardo Fibonacci was a well-travelled Italian who introduced the concept of zero and the Hindu-Arabic numeralsystem to Europe in 1200AD. Healso described the Fibonacci sequenceof numbers using an idealised breeding population of rabbits. Each rabbit pair produces another pair every month, taking one month firstto mature, and giving the
- 6. sequence 0,1,1,2,3,5,8,13,... Each number in the sequence is the sumof the previous two. Fibonacci spiral If you constructa series of squares with lengths equal to the Fibonacci numbers (1,1,2,3,5, etc) and trace a line through the diagonals of each square, it forms a Fibonacci spiral. Many examples of the Fibonaccispiral can be seen in nature, including in the chambers of a nautilus shell. Golden ratio (phi) The ratio of consecutive numbers in the Fibonacci sequence approaches a number known as the golden ratio, or phi (=1.618033989...). The aesthetically appealing ratio is found in much human architecture and plant life. A Golden Spiral formed in a manner similar to the Fibonacci spiralcan be found by tracing the seeds of a sunflower fromthe centre outwards.
- 7. Geometric sequence Bacteria such as Shewanella oneidensis multiply by doubling their population in size after as little as 40 minutes. A geometric sequencesuch as this, whereeach number is double the previous number [or f(n+1) =2f(n)] produces a rapid increasein the population in a very shorttime.
- 8. CONCLUSION Nature is innately mathematical, and she speaks to us in mathematics. We only have to listen. When we learn more about nature, it becomes increasingly apparent that an accurate statement about nature is necessarily mathematical. Anything else is an approximation. So, mathematics is not only science but is also an exact science. Because nature is mathematical, any science that intends to describe nature is completely dependent on mathematics. It is impossible to overemphasize this point, and it is why Carl Friedrich Gauss called mathematics "the queen of the sciences."
- 9. REFERENCE www.math.duke/edu www.project2061.org/publications/sfaa/online/chap2.html www.cimt.plymouth.ac.uk/projects/mepres/alevel/pure_ch 1.pdf