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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]

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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.

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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…..

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Types of Graphs

There are many types of graphs that we use in daily life but here we discuss only few types.

Circle graphLine graphPicture graphBar graphHistogram 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 )

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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.

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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

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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

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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:

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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

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Graph in Science & Technology

Graphs in Physics:

Graph of density.

Graph of Isotherm.

Stress-strain graph.

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Stress-strain graph.

Frequency vs. current graph in resonance circuit..

Charging of a capacitor graph.

Discharging of a capacitor graph.

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Work energy graph.

Pressure vs. time graph of heart beats.

Graph of interference on CRO.

Graph of critical angle.

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Graph of internal energy.

Graph of adiabatic process.

Graph of half life.

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Graphs in mathematics:Graph of parabola.

Graph of hyperbola.

Graph of vertical ellipse.

Graph of horizontal ellipse.

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Graph of sin function.

Graph of cosine function.

Graph of cos function.

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Graph of sec function.

Graph of tan function.

Graph of cot function.

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Graph in economy

Graph of normal profit.

Graph of intrest rate in market.

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Rent thoery graph of diferent lands.

Shut down point:

a point at which some loss to fix costs.