GEOMETRY in real life

Group – C

Definition

a branch of mathematics that deals with the

measurement, properties, and relationships of points, lines, angles, surfaces, and solids; broadly: the study

of properties of given elements that remain

invariant under specified transformations

In Other Words

What is Geometry?• Geometry is one of the classical

disciplines of math. • Roughly translating in Greek as "Earth Measurement", it is concerned with the properties of space and figures. • It is primarily developed to be a

practical guide for measuring lengths, areas, and volumes, and is still in use up to now.

These were the basics, Now back to the

topic!

When do we actually use

Geometry?

Topic #1

Area, Perimeter

and Volume

Area problems are one of the most common uses of geometry in our everyday lives. Let's say you need to install new carpet in your bedroom. How much carpet will you need to buy? Measure your room's length and width and then multiply

them together to find out how many square feet of carpeting is needed. This is represented by the formula A = L x W, or

area equals length times width. If, for example, your room is 12 feet by 10 feet, you will need

120 square feet of carpet.

Another area problem you may encounter is determining how

many cans of paint to buy to cover your walls. The label on the gallon of paint tells you it will cover 400

square feet. You measure your walls and find that the room you

want to paint has walls of the following dimensions: 10 ft x 10 ft, 10 ft x 8 ft, 10 ft x 10 ft and 10 ft x

8 ft. So you need to cover the areas of 100 square feet + 80

square feet + 100 square feet + 80 square feet = 360 square feet.

Your room can be single coated by one can of paint.

Perhaps you are planning a garden. A bag of fertilizer says it can cover 100 square feet. You need to know how many bags you will need. Measure

the area of your garden (length times width) to find

your area. Let's say my garden measures 40 feet by 20 feet. That means I need to cover 800 square feet of area with fertilizer. Divide 800 by 100

and you get 8. We need 8 bags of fertilizer for my garden.

Let's say you want to

fence a garden.

Find the perimeter to answer this question. Add up

all four sides to get the perimeter - 40 +20 + 40 + 20 = 120 feet. You will need 120

feet of fencing to enclose your garden.

You could use volume to find out how much cement mix it will take to pour a walkway or how much sand is needed to fill a

sandbox.

Let's look at the sandbox example. You have built a sandbox that is 5 feet

long by 5 feet wide. The sides are 6 inches tall. Volume is length times

width times height or V = L x W x H. Six inches equals one half of a foot, or 0.5 feet. Our equation would be 5 x 5

x 0.5 = 12.5 cubic feet. It will take 12.5 cubic feet of sand to fill our

sandbox. A fifty pound bag of sand is approximately half a cubic foot, so 25

bags would fill the sandbox completely full, or 12 and 1/2 bags

would fill it half full, leaving room for sand toys and kids.

Topic #2

Uses of geometry in

various occupations

A mechanical engineer designs machines ranging from tiny

gear sets to large construction cranes. Using geometry, he

determines the strongest shapes for mechanical parts. He

calculates the area, weight and volume of pieces and ensures that a machine's thousands of moving

parts fit together and don't interfere with one other.

Mechanical Engineer

A surveyor uses trigonometry, a branch

of geometry, to measure distances and angles between points on land.

Trigonometry uses the mathematical properties of right triangles; by measuring

one angle and one distance, the surveyor can calculate the lengths of

the other sides and the angles between them. While computerized and automated

equipment now does the actual work of calculation, the surveyor must understand the principles behind the calculations to

perform the measurements correctly.

Surveyor

A mathematician uses sophisticated conceptual tools to investigate the

properties of shapes. Using proofs, which justify geometric ideas in

a clear, step-by-step manner, he lays the mathematical foundations for new ideas in geometry. The mathematician

then publishes these ideas, and people of other occupations adopt

them in useful ways. The mathematician also educates and trains students in using geometry, proofs and

mathematical concepts.

Mathematician

Many of the ideas an astronomer uses are applications of geometry. As stars

and galaxies form, they settle into shapes such as spheres and discs that conform to their

mass, their composition and the force of gravity. An

astronomer studies the elliptical orbits of comets, asteroids and planets; to

find exact answers to questions about their speed and location, she uses the mathematical properties of ellipses.

Astronomer

A graphic designer studies how basic geometric shapes combine into artistic visual layouts in two

and three dimensions. A graphic artist uses geometric concepts such as

perspective and golden ratios to create the most pleasing designs. He uses

computer graphical tools that break complex, realistic images into many

basic circles, lines and polygons.

Graphic Designer

• Computer imaging, something that is used nowadays for creating animations, video games, designing, and stuff like that, are created using geometric concepts.

• Also, geometry is used in mapping. Mapping is an essential element in professions such as surveying, navigation, and astronomy. From sketching to calculating distances, they use geometry to accomplish their job.

• In addition, professions such as medicine benefit from geometric imaging. Technologies such as CT scans and MRIs are used both for diagnosis and surgical aids. Such methods enable doctors to do their job better, safer, and simpler.

Some more occupations in which geometry is used

As you can see, geometry

affects us even in the most basic details of

our lives. No matter what the form, it helps us understand specific phenomena and it

helps us in uplifting the quality of life.

THANK YOU!