ONLINE SUBMISSION OF ASSIGNMENT

CONGRUENCE AND SIMILARITY CONCEPTS IN NATURE /

ENVIRONMENT

PREPARED BY

K.V.PADMAJAB.Ed MATHEMATICS

Introduction:

“In this changing world, those who understand and can do mathematics will have significantly enhanced prospects and options for shaping their futures. Mathematical competence opens doors that produce opportunities. A lack of mathematical competence keeps those doors closed. All students should have the opportunity and the support necessary to learn mathematics with depth and understanding”

The application of Mathematics can be found all around us - in our daily lives, in the natural environment that we live in. Studying the congruency and similarity in nature is the aim of this assignment. The aim is to understand whether there are mathematical concepts in nature

If you ever have to build something you'll use these principles. There are a lot of triangles in real life applications. Scale models use these principles as well, and they're also necessary for data extrapolation, mathematical modelling, engineering... there are many, many applications that use these simple principles.

I shall be discussing about the same in this assignment.

Definitions:

“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 Slides, then the shapes are Congruent :

“Shapes are similar if they have the 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).

Congruent or Similar?

- The two shapes need to be the same size to be congruent.

- When we need to resize one shape to make it the same as the other, the shapes are Similar

When We Then the Shapes are….

Only Rotate, Reflect and/or Translate CongruentAlso need to Re-size Similar

Whether shapes are congruent or similar can be found by comparing their internal angles and the length of their sides.

Congruence and Similarity concepts found in Nature:

1. Leaf: In a tree all leaves will be similar. Also, when we consider one leaf, the midrib and the lines on the two sides are same. Hence congruent

Even in a Coconut Leaf, the big leaves are equally distributed both sides and the lines are congruent on both sides

2. Buildings: Consider Villa houses, almost all are same in area and size. We can find proof for congruency and similarity even within one building where the alignment of pillars etc are congruent. A few other strikingly congruent buildings are Tajmahal, Bridges, Towers, Pyramids etc

3. Insects: Butterflies, with their beautiful wing designs are an example of congruency and similarityThere is congruency in the way their entire form is designed by nature – the whiskers, the size and shape of both sides of its wings and the designs within them aswell.

4. Fruits and Vegetables: Citrus fruits like lemons, oranges, peaches etc and Pea Pods display congruency and similarity through the alignment of their seeds and pods.

5. Garden and Pathways are other places where we can find the mathematics of congruency and similarityThe alignment of the trees, the way the pathways are laid are all examples to the topic of our discussion.

6. Books – whose area, shape, size, angle, elevation etc. are perfect examples of congruency and similarity in everyday life. Also, when we look at poems, they have a specific methodology to making them sounding poetic – be it Sonnets or Tirukural with the display of similarity in the arrangements of the verses itself and the words in the first and second line

7. Earrings – Its fancy how there is mathematics in everything. Consider the pairs of earrings below. They are a perfect example of congruency and similarity

8. Automobiles – The engineering behind the development of the abutomobiles ensure the congruency and similarity be it the tyres or the windows or many parts that make the vehicle move

9. Science – How can we not mention about the scientific “congruency and similarity” found our own body? Our Hands, the skeletal system etc. are perfect and accurate reflections of the topic discussed. Also, we can find congruence in similarity in the structure of our DNA and chromosomes as well. These are merely a few examples in the vast universe of such existence of the concept.

Conclusion:

Mathematics is a science that is all around us. Understanding the concepts of mathematics will enable people handle their everyday situations and resources better.

The concept of congruence is not restricted to the study of geometry. It plays an important role in everyday living. We may be able to buy a refill for our pen when the ink runs dry. We use congruence to replace a worn out part of the car, looking for the 'same part number'. In construction, they have to use the blocks of a 'standard size'. When using screws, we look for the kind of screw that we need and also screwdriver that fits. In each of these examples, the idea of sameness of shape and sizes applies.

After reading this assignment, the learners will be able to link the mathematical concepts to the objects they see around in nature. They will also be able to appreciate the influence of mathematics in their day to day life. It will also create an interest in them to know more about the correlation of mathematics and mathematical concepts in our environment.

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