11
GraphGraph
Presented to:Presented to:
Sir Atif FirdausSir Atif Firdaus
Presented ByPresented By::
MALIK GHULAM MURTZAMALIK GHULAM MURTZA
Roll No: 9226Roll No: 9226
Department of Computer ScienceDepartment of Computer Science
Garrison Post Graduate College [M]Garrison Post Graduate College [M]
2
GRAPHS & THEIR
HISTORY
Early History:
L.J.Henderson, attempted to analyze
mammalian blood solely as a physical-chemical
substance. He found that the only way he could
describe a chemical system as complicated as
blood was by a diagram called a "nomogram“.
This lecture tells the history of graphs in the
eighteenth century, their development in
nineteenth-century engineering practice, and
their importance in the twentieth century.
NOMOGRAM: a graphic representation of numerical
relations .
MAMMALIAN: of or relating to the class Mammalian.
GRAPH THEORY: This theory is also given by Euler
(1707-1783) in this regard.
3
WHAT IS
GRAPH?
The word "graph" has many definitions as:
1)In elementary mathematics, "graph" refers
to a function graph or "graph of a function," i.e.,
A plot of a function i.e., trigonometric function
etc…
2) Graphs are pictures that help us understand
amounts. (Or) A graph is a diagrammatic
technique to exhibit information. These amounts
and information are called data.
NOTE:- Elementary Mathematics consists of
mathematics topics frequently taught at the
primary or secondary school levels. The most
basic topics in elementary mathematics are
arithmetic and geometry…..
4
Types of
Graphs
There are many types of graphs that we use in
daily life but here we discuss only few types.
Circle graph
Line graph
Picture graph
Bar graph
Histogram
Histogram is special type of bar graph.
(The word histogram comes from the
Greek histos, meaning pole or mast, and
gram, which means a chart or graph, was
first introduced by Karl Pearson )
5
Circle or Pie
graph
A circle graph is shaped
like a circle. It is divided
into fractions that look
like pieces of pie, so
sometimes a circle graph
is called a pie graph.
Many times the fractional
parts are different colors
and a key explains the
color.
Example :if we have some
fruits than liking of
different people is given
in the pie chart.
6
Line graph
A line graph shows
points plotted on a
graph. The points are
then connected to form
a line.
Example: The table
upper aside shows daily
temperatures for New
York City, recorded for
6 days, in degrees
Fahrenheit, as shown in
the line graph given
aside below.
Temperatures In NY City
Day Temperature
1 43° F
2 53° F
3 50° F
4 57° F
5 59° F
6 67° F
7
Picture graph
A picture graph uses
pictures or symbols to
show data. One picture
often stands for more than
one vote so a key is
necessary to understand
the symbols.
Example : Inside a Picture
Graph is shown.
Key :Each Book represents
1 Book .
A table is also shown that
tells us about no of books
which everyone have.
NAME NUMBER OF
BOOKS
JIM 2
TOM 4
HARRY 3
MIKE 6
8
Bar Graph
A graph used to visually
display frequencies or
percentages and can be used
to compare data are called
Bar graph. (or)
A graph drawn using
rectangular bars to show how
large each value is.
The bars can be horizontal or
vertical.
Example :if we have the set
{1,2,2,3,3,3,3,4,4,5,6}, we can
graph them vertically like
this:
9
Apllications of graphs
in general life
Graphs are used in almost every field of life due to
amazing success of the world, Especially in
following fields:
Science & technology
Economy
Banking & finance
10
Graph in Science & Technology
Graphs in
Physics:
Graph of density.
Graph of Isotherm.
Stress-strain graph.
11
Stress-strain graph.
Frequency vs. current graph
in resonance circuit..
Charging of a capacitor
graph.
Discharging of a capacitor
graph.
12
Work energy graph.
Pressure vs. time graph
of heart beats.
Graph of interference on
CRO.
Graph of critical angle.
13
Graph of internal energy.
Graph of adiabatic
process.
Graph of half life.
14
Graphs in mathematics:
Graph of parabola.
Graph of hyperbola.
Graph of vertical ellipse.
Graph of horizontal
ellipse.
15
Graph of sin function.
Graph of cosine function.
Graph of cos function.
16
Graph of sec function.
Graph of tan function.
Graph of cot function.
17
Graph in economy
Graph of normal profit.
Graph of intrest rate in
market.
18
Rent thoery graph of
diferent lands.
Shut down point:
a point at which some
loss to fix costs.

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Introduction to Graph in general life

  • 1. 11 GraphGraph Presented to:Presented to: Sir Atif FirdausSir Atif Firdaus Presented ByPresented By:: MALIK GHULAM MURTZAMALIK GHULAM MURTZA Roll No: 9226Roll No: 9226 Department of Computer ScienceDepartment of Computer Science Garrison Post Graduate College [M]Garrison Post Graduate College [M]
  • 2. 2 GRAPHS & THEIR HISTORY Early History: L.J.Henderson, attempted to analyze mammalian blood solely as a physical-chemical substance. He found that the only way he could describe a chemical system as complicated as blood was by a diagram called a "nomogram“. This lecture tells the history of graphs in the eighteenth century, their development in nineteenth-century engineering practice, and their importance in the twentieth century. NOMOGRAM: a graphic representation of numerical relations . MAMMALIAN: of or relating to the class Mammalian. GRAPH THEORY: This theory is also given by Euler (1707-1783) in this regard.
  • 3. 3 WHAT IS GRAPH? The word "graph" has many definitions as: 1)In elementary mathematics, "graph" refers to a function graph or "graph of a function," i.e., A plot of a function i.e., trigonometric function etc… 2) Graphs are pictures that help us understand amounts. (Or) A graph is a diagrammatic technique to exhibit information. These amounts and information are called data. NOTE:- Elementary Mathematics consists of mathematics topics frequently taught at the primary or secondary school levels. The most basic topics in elementary mathematics are arithmetic and geometry…..
  • 4. 4 Types of Graphs There are many types of graphs that we use in daily life but here we discuss only few types. Circle graph Line graph Picture graph Bar graph Histogram Histogram is special type of bar graph. (The word histogram comes from the Greek histos, meaning pole or mast, and gram, which means a chart or graph, was first introduced by Karl Pearson )
  • 5. 5 Circle or Pie graph A circle graph is shaped like a circle. It is divided into fractions that look like pieces of pie, so sometimes a circle graph is called a pie graph. Many times the fractional parts are different colors and a key explains the color. Example :if we have some fruits than liking of different people is given in the pie chart.
  • 6. 6 Line graph A line graph shows points plotted on a graph. The points are then connected to form a line. Example: The table upper aside shows daily temperatures for New York City, recorded for 6 days, in degrees Fahrenheit, as shown in the line graph given aside below. Temperatures In NY City Day Temperature 1 43° F 2 53° F 3 50° F 4 57° F 5 59° F 6 67° F
  • 7. 7 Picture graph A picture graph uses pictures or symbols to show data. One picture often stands for more than one vote so a key is necessary to understand the symbols. Example : Inside a Picture Graph is shown. Key :Each Book represents 1 Book . A table is also shown that tells us about no of books which everyone have. NAME NUMBER OF BOOKS JIM 2 TOM 4 HARRY 3 MIKE 6
  • 8. 8 Bar Graph A graph used to visually display frequencies or percentages and can be used to compare data are called Bar graph. (or) A graph drawn using rectangular bars to show how large each value is. The bars can be horizontal or vertical. Example :if we have the set {1,2,2,3,3,3,3,4,4,5,6}, we can graph them vertically like this:
  • 9. 9 Apllications of graphs in general life Graphs are used in almost every field of life due to amazing success of the world, Especially in following fields: Science & technology Economy Banking & finance
  • 10. 10 Graph in Science & Technology Graphs in Physics: Graph of density. Graph of Isotherm. Stress-strain graph.
  • 11. 11 Stress-strain graph. Frequency vs. current graph in resonance circuit.. Charging of a capacitor graph. Discharging of a capacitor graph.
  • 12. 12 Work energy graph. Pressure vs. time graph of heart beats. Graph of interference on CRO. Graph of critical angle.
  • 13. 13 Graph of internal energy. Graph of adiabatic process. Graph of half life.
  • 14. 14 Graphs in mathematics: Graph of parabola. Graph of hyperbola. Graph of vertical ellipse. Graph of horizontal ellipse.
  • 15. 15 Graph of sin function. Graph of cosine function. Graph of cos function.
  • 16. 16 Graph of sec function. Graph of tan function. Graph of cot function.
  • 17. 17 Graph in economy Graph of normal profit. Graph of intrest rate in market.
  • 18. 18 Rent thoery graph of diferent lands. Shut down point: a point at which some loss to fix costs.