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
4. 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
8. 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
9. 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.
10. 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.
11. 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.
12. will take to pour a walkway or how much sand is needed to fill a
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
14. Mechanical Engineer
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.
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
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.
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.
18. Graphic Designer
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.
19. Some more occupations in which
geometry is used
• 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
20. 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.