This document discusses the mathematical aspects found in natural environmental phenomena. It provides examples of congruence seen in identical flowers or leaves of the same plant. Similarity is discussed with examples like pinecone spirals and same-plant flowers having proportionate dimensions and shape. Geometric shapes in nature are examined like honeycomb, pineapple, and ladies finger. Ratio and proportion are evident in distances like eye to chin and eye to mouth. Symmetry is described and examples given like butterflies, insects, and leaves being exactly alike but for orientation. The document concludes mathematical models can describe the environment and factors affecting it to enable predictions.

1. MATHEMATICS
ASSIGNMENT
Submitted by, Submitted on,
ANILA RAJU.R 15/6/2014
ROLL NO: 1
CHRIST NAGAR COLLEGE
OF EDUCATION, TVM - 27

2. NATURAL RESOURCES -Mathematical Aspects
Found In Environmental Phenomena
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congruence
operty
.

3. INTRODUCTION
athematics is a way of describing the 'real' world so that
predictions and insights and explanations become easier.
Mathematical models are used in computing. Environment is a 'system’
word meaning the things that affect the system. But that the system
cannot change. It is used much more generally to mean all things that
surround or things with which there are interactions. A natural
resource is anything that people can use which comes from nature.
People do not make natural resources, but gather them from the each
examples of natural resources are air, water, wood, oil etc. Among them
we can see the mathematical aspects such as similarities, geometrical
shapes, ratio and proportion etc. Here we are going to discuss about the
mathematical aspects found in environment.
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4. NATURAL RESOURCES -Mathematical Aspects
Found In Environmental Phenomena
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CONGRUENCE:
Any two geometric figures are said to be congruent if they can be
made to coincide ( fit exactly on each other ) .Congruent means exactly
agreeing .They are exactly alike in all respects of figures having all
corresponding parts equal. Congruency are mostly proved by
superimposition. So any figure can be exactly reproduced anywhere. The
congruence can be seen even in nature. There are so many examples for
that. Examples are as following.
Example:
Flowers or leaves of a same plant.

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SIMILARITY:
Similar figures are related to one another in the same way as a lanthern
slide and its projection on a screen. Similar figures are figures of the
same appearance, irrespective of their size. Similarity applies to
surface (and solids) rather than lines. Two conditions only are requisite
for similarity,
1. The same shape
2. Proportionate dimensions
Both conditions are generally necessary.
Example:
(i)Pinecone
We can see some of the same fractality in the spirals of pinecone
seeds.
(ii) Flowers of a same plant

7. GEOMETRIC SHAPES:
Geometry is the study of properties of shapes, for example circle,
triangle, and squares and is used to reach conclusions about the size of
angles and lengths of lines. Geometry is not restricted to shapes in two
dimensions and many results used in two dimensions can be extended to
three dimensional situation. In nature we can see different geometrical
shapes. We can see different geometrical figures in nature. Below is
the some of the examples that can be viewed in nature.
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Example:
(i)Honey comb
(ii) Pineapple

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(iii)Ladies finger
RATIO AND PROPORTION:
Ratio is the number which gives the relation of a certain quantity to
another quantity. When four terms are so related that the ratio of the
first to the second is the same as the ratio of the third to fourth ,
they are said to be in proportion.
Example:
(i)Distance of our eyes to chin with a distance of eye to mouth

9. (ii)A golden spiral describes the structure of Hurricane.
SYMMETRIC PROPERTY
Stand in front of looking glass with a book in your right hand. In the
glass you see an image of yourself, but the image holds the book in left
hand. Close your left eye, the image closes its right eye. The image of
your right hand is a left hand. Right and left handed patterns that can
be folded exactly together and are thus images of each other, are said
to be symmetrical. Symmetrical figures are exactly alike in all respects
save one. If an apple is cut into two equal parts and parts are not
separated, the apple is symmetric with respect to the plane which
divides it.
(i)Butterflies
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(ii)Insects
(iii)Leaves

11. CONCLUSION
nvironment is used commonly to mean the biosphere, the
interrelated living part of our world and the parts of our world
that living things depends on. Mathematical models can describe
parts of our environment and factors that affect it. This enables
predictions to be made.
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12. REFERENCE
 answers.ask.com/science/nature
 The Teaching of Mathematics-S.M.AGGARWAL
 The Teaching of Mathematics-KULBIR SINGH SIDHU
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