This document provides an overview of geometry and how it is used. It acknowledges sources and indicates this presentation is for student benefit only. Geometry studies size, shape, and spatial relationships. It is used in computer graphics, engineering, robotics, medical imaging, and other fields. Examples of geometric structures in buildings like wigwams, skyscrapers, and cars are presented. Symmetry is also discussed as an important geometric concept seen in nature and science.

2. Acknowledgement :
 Information and pictorial illustrations to create
this work have been drawn from class notes,
prescribed text books and various internet
resources. The author gratefully acknowledges
the same. Any objections to the use of internet
resources may please be indicated to
suddurocks@yahoo.in so that the same
can be removed from the illustrations used in
this file.
 This presentation is created with the sole
intention of benefitting a large number of
student community. This may not be used for
any commercial purpose.

3. About
 Geometry is a part of mathematics concerned
with questions of size, shape, and relative
position of figures and with properties of
space. Geometry is one of the oldest sciences.

4. Geometry Is Used In :
 Computer Graphics - It is based on geometry,
how images are transformed when viewed in
various ways.

5.  Computer Aided Geometric Design -
Representing shapes in computers, and using
these descriptions to create images, to instruct
people or machines to build the shapes, etc.

6.  Robotics - In planning how to grasp a shape with
a robot arm, or how to move a large shape
without collision.

7.  Medical Imaging - How to reconstruct the shape
of a tumour from CAT scans, and other medical
measurements. Lots of new geometry and
other math was (and still is being) developed for
this.

8.  Structural Engineering - What shapes are rigid
or flexible, how they respond to forces and
stresses. Statics (resolution of forces) is
essentially geometry. This goes over into all
levels of design, form, and function of many
things.

9.  Protein Modeling - Much of the function of a
protein is determined by its shape and how the
pieces move. Mad Cow Disease is caused by the
introduction of a 'shape' into the brain (a shape
carried by a protein). Many drugs are designed
to change the shape or motions of a protein -
something that we are just now working to
model, even approximately, in computers, using
geometry and related areas (combinatorics,
topology).

10.  Physics, Chemistry, Biology - Symmetry is a
central concept of many studies in science - and
also the central concept of modern studies of
geometry. Students struggle in university
science if they are not able to detect symmetries
of an object (molecule in stereo chemistry,
systems of laws in physics, ... ). the study of
transformations and related symmetries has
been, since 1870s the defining characteristic of
geometric studies.

11. Pictures of Geometry in Real
World
 Geometry is used everywhere. Everywhere in
the world there is geometry, mostly made by
man. Most man made structures today are in
a form of Geometric.

12.  How, you ask? Well some examples would the a
CD, that is a 3-D circle and the case would be a
rectangular prism. Buildings, cars, rockets,
planes, maps are all great examples.

13. Examples On How The World Uses
Geometry In Buildings And Structure
 This is a picture with some basic geometric
structures.

14.  This is a modern reconstruction of the
English Wigwam. As you can there the
door way is a rectangle, and the wooden
panels on the side of the house are
made up of planes and lines. Except for
really planes can go on forever. The
panels are also shaped in the shape of
squares. The house itself is half a
cylinder.

15.  Here is another modern reconstruction of a
English Wigwam.

16.  This house is much similar to the one
before. It used a rectangle as a doorway,
which is marked with the right angles.
The house was made with sticks which
was straight lines at one point. With the
sticks in place they form squares when
they intercepts. This English Wigwam is
also half a cylinder.

17.  This is a modern day skyscraper at MIT.

18.  The openings and windows are all made
up of parallelograms. Much of them are
rectangles and squares. This is a
parallelogram kind of building.

19.  This is the Hancock Tower, in Chicago.

20.  With this image, we can show you more
3D shapes. As you can see the tower is
formed by a large cube. The windows
are parallelogram. The other structure is
made up of a cone. There is a point at
the top where all the sides meet, and
There is a base for it also which makes it
a cone.

21.  This is another building at MIT.

22.  This building is made up of cubes,
squares and a sphere. The cube is the
main building and the squares are the
windows. The doorways are rectangle,
like always. On this building There is a
structure on the room that is made up of
a sphere.

23.  This is the Pyramids, in Indianapolis.

24.  The pyramids are made up of pyramids,
of course, and squares. There are also
many 3D geometric shapes in these
pyramids. The building itself is made up
of a pyramid, the windows a made up of
tinted squares, and the borders of the
outside walls and windows are made up
of 3D geometric shapes.

25.  This is a Chevrolet SSR Roadster Pickup.

26.  This car is built with geometry. The
wheels and lights are circles, the doors
are rectangular prisms, the main area
for a person to drive and sit in it a half a
sphere with the sides chopped off which
makes it 1/4 of a sphere. If a person
would look very closely the person
would see a lot more shapes in the car.
Too many to list.

27. Symmetry
 Symmetry in common usage generally
conveys two primary meanings.

28.  The first is an imprecise sense of harmonious or
aesthetically-pleasing proportionality and
balance; such that it reflects beauty or
perfection.

29.  The second meaning is a precise and well-
defined concept of balance or "patterned self-
similarity" that can be demonstrated or proved
according to the rules of a formal system: by
geometry, through physics or otherwise.

30. Thank You !!!
Compiled By :
Sudarshan.S.K.
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