"Application of 3D and 2D geometry" explains the importance of geometry in our lives. Geometry is found everywhere from nature to human made machines. I have tried to inculcate all its applications. I hope it helps in providing guidance to those who are aspiring to understand geometry. I have taken help from internet and some books to acquire knowledge. thank you for clicking my slide.

1. APPLICATIONS OF 3D and 2D
GEOMETRY in DAILY LIFE..

2. Introduction
• What is geometry?
• Its importance
• History of geometry
Geometry in architecture
• Laksham jhula and other examples
• Golden Section
• Egyptian Architecture
• Islamic Architecture
Geometry in Daily Life
• In Nature
• In sports
• Computer graphics
• In astronomy

3. What is Geometry?
It is a branch of mathematics which is
concerned with questions of shape,
size, relative position of figures,
and the properties of space.

4. Importance of Geometry
• We are able to understand the wonder of the worlds shape as
well as appreciate it with the help of geometry.
• The construction of building require a major use of geometry.
• Many different scientific and technological fields require
knowledge of geometry. Especially in the more advanced and
specialized study fields the use and knowledge of Geometry is
essential to excelling.
• Two and three Dimensional shapes are originated in
geometry. The use of triangles and other shapes strongly
influence this. In the fields of television, movies and even little
things like puzzles or books all are influenced by geometry.

5. HISTORY OF GEOMETRY
• The earliest recorded beginnings of geometry can be traced to
ancient Mesopotamia and Egypt in the 2nd millennium BC.
• Early geometry was a collection of empirically discovered principles
concerning lengths, angles, areas, and volumes, which were developed to
meet some practical needs.
• Geometric procedures anticipated the Oxford Calculators, including
the mean speed theorem, by 14 centuries. South of Egypt the ancient
Nubians established a system of geometry including early versions of sun
clocks.
• In the 7th century BC, the Greek mathematician Thales of Miletus used
geometry to solve problems such as calculating the height of pyramids and
the distance of ships from the shore. He is credited with the first use of
deductive reasoning applied to geometry.
• Indian mathematicians also made many important contributions in
geometry. The Satapatha Brahmana (3rd century BC) contains rules for
ritual geometric constructions that are similar to the Sulba Sutras.
• In the Middle Ages, mathematics in medieval Islam contributed to the
development of geometry, especially algebraic geometry.

6. What is 2D Geometry?
• Two perpendicular coordinate
axes are given which cross each
other at the origin. They are
usually labeled x and y. Relative
to these axes, the position of any
point in two-dimensional space is
given by an ordered pair of real
numbers, each number giving the
distance of that point from
the origin measured along the
given axis, which is equal to the
distance of that point from the
other axis.

7. What is 3d Geometry?
Three-dimensional space is a geometric setting in
which three values are required to determine the
position of an Three-dimensional space (also: 3-
space or, rarely, tri-dimensional space).

8. Geometry in Architecture
Architectural Geometry is an area of research
which combines applied geometry and architecture,
which looks at the design, analysis and manufacture
processes. It lies at the core of architectural design and
strongly challenges contemporary practice, the so
called architectural practice of the digital age.

9. Can you find the Golden Section
within?

11. What is the Golden Section?
• The Golden Section refers to rectangles that have a
ratio of 1:1.6. This means that if the width of a
rectangle is 1 foot long, the length will be 1.6 feet long.
(The number 1.6 is sometimes referred to as "phi", and
it looks like the letter o with a line through it (ø).
• The Golden Section (or Golden Ratio or Golden Mean
or Golden Rectangle) appears in a lot of ancient Greek
architecture and has been analyzed extensively by the
famous mathematician Fibonacci. The ratio of 1:1.6 is
said to be "pleasing to the eye."

12. Visit page View image
Egyptian Geometry
• The Great Pyramid of Egypt closely embodies Golden
Ratio proportions but there is debate as to the
geometry used in the design of the Great Pyramid of
Giza in Egypt it was once flat, smooth outer shell is
gone and all that remains is the roughly-shaped inner
core, so it is difficult to know with absolute certainty.
The outer shell remains though at the cone, so this
does help to establish the original dimensions. There
is evidence, however, that the design of the pyramid
may embody these foundations of mathematics and
geometry:
• Phi, the Golden Ratio that appears throughout
nature.
• Pi, the circumference of a circle in relation to its
diameter.
• The Pythagorean Theorem – Credited by tradition to
mathematician Pythagoras (about 570 – 495 BC),
which can be expressed as a² + b² = c².

13. Ancient Rome: Vitruvius
• The influential Ancient Roman architect Vitruvius argued that
the design of a building depends on two qualities, proportion
and symmetria.
• Proportion ensures that each part of a building relates
harmoniously to every other part.
• Symmetria in Vitruvius's usage means something closer to
the English term modularity than mirror symmetry.
• In his Basilica at Fano, he uses ratios of small integers,
especially the triangular numbers(1, 3, 6,10, ...) to proportion
the structure into modules.
• Thus the Basilica's width to length is 1:2; the aisle around it is
as high as it is wide, 1:1; the columns are five feet thick and
fifty feet high, 1:10.

14. Vitruvius
designs

15. Meenakshi Temple
• Vaastu Shastra, the ancient Indian canons of architecture and town
planning, employs symmetrical drawings. Complex calculations are used to
arrive at the dimensions of a buildingand its components.
• The designs are intended to integrate architecture with nature, the relative
functions of various parts of the structure, and ancient beliefs utilizing
geometric patterns ,symmetry and directional alignments.
• The mathematics of fractals has been used to show that the reason why
existing buildings have universal appeal and are visually satisfying is
because they provide the viewer with a sense of scale at different viewing
distances.
• For example, in Hindu temples such as the Virupaksha Temple built in the
seventh century, the whole have the same character, with fractal
dimension in the range 1.7 to 1.8. The cluster of smaller towers about the
tallest, central, tower which represents the holy Mount Kailash, abode of
Lord Shiva, depicts the endless repetition of universes in Hindu
cosmology.

16. Meenakshi Temple

17. Geometry in Modern Architecture
• Mughal architecture, as seen in the abandoned imperial city of Fatehpur
Sikri and the Taj Mahal complex, has a distinctive mathematical order and
a strong aesthetic based on symmetry and harmony.
• The Taj Mahal exemplifies Mughal architecture, both
representing paradise and displaying the Mughal Emperor Shah Jahan's
power through its scale, symmetry and costly decoration.
• The buildings include a mosque in red sandstone on the west, and an
almost identical building, the Jawab or 'answer' on the east to maintain
the bilateral symmetry of the complex.
• The Taj Mahal complex was laid out on a grid, subdivided into smaller
grids. The historians of architecture Koch and Barraud agree with the
traditional accounts that give the width of the complex as 374 Mughal
yards or gaz ,the main area being three 374-gaz squares. These were
divided in areas like the bazaar and caravanserai into 17-gaz modules; the
garden and terraces are in modules of 23 gaz, and are 368 gaz wide (16 x
23).

19. Jantar Mantar
• The Jantar Mantar is an equinoctial sundial, consisting
a gigantic triangular gnomon with
the hypotenuse parallel to the Earth's axis. On either
side of the gnomon is a quadrant of a circle, parallel to
the plane of the equator. The instrument is intended to
measure the time of day, correct to half a second
and declination of the Sun and the other heavenly
bodies.
• There are five Jantar Mantar monuments in India, of
which the largest is in Jaipur which features many
instruments along with the world's largest stone
sundial. The Vrihat Samrat yantra is a sundial that can
give the local time to an accuracy of 2 seconds.

20. The Taj Mahal
• Golden section Φ was used in the construction of the Taj Mahal,
•Called a monument to love, the Taj Mahal has also been called "Indias
most famous and finest example of architecture.
• We could call it a monument to symmetry.
•From the formal gardens divided into four sections, to the tomb 900
feet from the entrance, the four minarets continue this symmetrical
theme.
•The minarets next to the Taj Mahal are 41.1meters or 137 feet high
and are cylindrical columns with angles.
•Located at each of the corners of the raised marble plinth the
minarets repeat the right angles that are an obvious part of the Taj
Mahal.
•The main structure is cubical.
•The windows have arches which comes to a point.

23. Parthenon
• The Parthenon is 69.5 metres (228 ft) long, 30.9 metres (101 ft) wide and 13.7
metres (45 ft) high to the cornice. This gives a ratio of width to length of 4:9, and
the same for height to width. Putting these together gives height:width:length of
16:36:81, or to the delight. of the Pythagoreans 42:62:92. This sets the module as
0.858 m.
• A 4:9 rectangle can be constructed as three contiguous rectangles with sides in
the ratio 3:4. Each half-rectangle is then a convenient 3:4:5 right triangle, enabling
the angles and sides to be checked with a suitably knotted rope.
• The inner area similarly has 4:9 proportions (21.44 metres (70.3 ft) wide by 48.3 m
long); the ratio between the diameter of the outer columns, 1.905 metres (6.25 ft),
and the spacing of their centers, 4.293 metres (14.08 ft), is also 4:9.

24. Geometry in Art
• Besides the Mona Lisa, the Golden Ratio number 1.618 was used in the
planning and construction of religious structures as well as for sacred
spaces. Apparently, da Vinci methodically laid out his composition before
he started to paint in order to align his model while using a camera
lucida as suggested by artist David Hockney.
• Just as the Golden Section is found in the design and beauty of nature, it
can also be used to achieve beauty and balance in the design of art. The
Golden Section was used extensively by Leonardo Da Vinci. All the key
dimensions of the room, the table and ornamental shields in Da Vinci’s
“The Last Supper” were based on the Golden Ratio, which was known in
the Renaissance period as The Divine Proportion.
• Leonardo Da Vinci explored the human body involving in the ratios of the
lengths of various body parts. He called this ratio the “divine proportion”
and featured it in many of his paintings. It is believed that Leonardo, as a
mathematician tried to incorporate of mathematics into art. The Mona
Lisa painting seems to be made purposefully line up with golden rectangle.
In a nutshell he knew and used this to achieve beauty, harmony and
balance.

26. Other examples of
architecture in which
geometry is used

31. GEOMETRY IN NATURE
• In the world of natural phenomena, it is the underlying
patterns of geometric form, proportion and associated wave
frequencies that give rise to all perceptions and
identifications.
• Different fruits, leaves and flowers have geometrical
shape depending upon the area in which they are found.
For example, pine leaves are thin and have sharp tip
giving it a shape like coneFruits like oranges, lemon
are spherical in shape whereas cashew fruits have a
peculiar shape like in kiwi, orange, apple etc.
• Even vegetables have different geometric shapes, like
carrot, radish are conical in shape whereas beetroot,
tomato, onion are spherical in shape.

33. GEOMETRY IN SPORTS
• In every sports geometry is a vital part from sports
material to the ground where it is played. For example
basketball is spherical in shape and the place where it
is played is square in shape.
• Relay Race is played in an oval shaped racing track and
the stick is cylindrical in shape.
• In carom, the board is rectangular in shape whereas
the coins are circular in shape. All the boards and play
area for each sports is measured and made under
some geometrical theory and principles.

34. Geometry in astronomy
• In astronomy, geometric shapes help to
understand the location of different planets,
solar system, and different stars.
• Our planets are spherical in shape. The orbits
are oval in shape. Many geometrical principles
and equipments are used in astronomy.
• Many important calculations and finding
made in astronomy is possible with the help

35. COMPUTER GRAPHICS
The appearance of an object depends largely on its
exterior, boundary representations are most commonly
used.
Two dimensional surfaces are a good representation
for most objects, though they may be non-manifold.
Since surfaces are not finite, discrete digital
approximations are used.
Polygonal meshes (and to a lesser extent subdivision
surfaces) are by far the most common representation,
although point-based representations have become
more popular recently (see for instance the Symposium
on Point-Based Graphics)