MATHEMATICS ASSIGNMENT SUBMITTED BY :ALEENA ALEXANDER OPTIONAL:MATHEMATICS REG NO:18014385001

ENVIRONMENTAL PHENOMENA MATHEMATICAL ASPECT FOUND IN ENVIRONMENTAL PHENOMENA

1.CONGRUENCE 2.SIMILARITY 3.RATIO AND PROPORTION 4.GEOMATRIC SHAPES 5.SYMMETRIC PROPERTY

1. INTRODUCTION Mathematics is the study of topics such as quantity,numbers,structure,space and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth by mathematical proof. Mathematics is used throughout the world as an essential tool in many fileds,including natural science, engineering ,medicine ,finance and social sciences, Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields ,Inspires and makes use of new mathematical discoveries , which has led to the development of entirely new mathematical disciplines such as statistics and game theory.

1. CONGRUENCE “Congruent shapes are the same shape and size as one another, but can be in different positions , orientations or form mirror images.” If one shape can become another using turns ,flips and /or slide then this shapes are congruent. “Shapes are similar if they have same proportions. They may have different positions and orientations” Two shapes are similar when the only difference is size( and possibly the need to turn or flip one around.)

Congruence in spectacles Congruence in hands

2. SIMILARITY Similar figures are related to one another in the same way as a lantern slides and its projection on a screen. Similar figures are figures of same appearance, irrespective of their size. Shapes are similar if they have same proportion.

LEAVES OF THE SAME PLANT FLOWERS OF THE SAME PLANT

3. RATIO AND PROPORTION A ratio is an indicated quotient of two quantities. Every ratio is a fraction and all ratios can be described by means of a fraction. The ratio of x and y is written as x:y, it can be represented as , Thus , x/y A proportion is the equality of two ratios. Example:-

Ratio in shell Ratio in rose flower

4. GEOMETRIC SHAPES Geometry is one of the oldest sciences and is concerned with questions of shape , size and relative position of figures and with properties of space. Geometry is considered as an important field of study because of its application in daily life. Some examples are:-

Stones in hexagonal shape Bangles in circle shape

5. Symmetric property Many mathematical principles are based on ideals and apply to an abstract, perfect word . This perfect word of mathematics is reflected imperfect physical world such as in the appropriate symmetry of a face divided by an axis along the nose

Symmetry in leaves Symmetry in a bird

CONCLUSION we can realize that maths in nature is factual in its tangibility. It is this outstanding quality that makes the use of maths in nature a tremendous resource for the classroom. Too often we force mathematical concepts on the basis of blind faith , while examples such as these are quite all around us.

REFERENCE Answers.ask.com/science/nature The Teaching of mathematics – S.M.AGGARWAL The Teaching of mathematics – KULBIR SING SIDHU