IntegersIntegersdone bydone by

6 A- group 36 A- group 3

sridattha.c-leader sridattha.c-leader vishwadutt vishwadutt

danica danica amog amog

sahana sahana dhanush dhanush

www-groups.dcs.st-and.ac.uk/~history.html www-history.mcs.st-and.ac.uk/

Mathematicians.htmlen.wikipedia.org/wikibooks.google.comwww.britannica.com/EBchecked/topic/77073

History of integers During the 600s, negative numbers were in

use in India to represent debits However ,in the 12th century in India ,

Bhaskara gives negative roots for quadratic equations but says the negative value ‘is in this case not to be taken , for it is inadequate; people do not approve of negative roots.’

As recently as the 18th century ,the Swiss mathematician leonard Euler believed that negative numbers were greater than infinity.

Inventors of integers Gerolamo Cardano BrahmaguptaFrancis MaseresWilliam friendsDe Morgan,Peacock

Negative integers are commonly seen in sports. Consider hockey

Each line of players records a plus or a minus.

If other team scores on your line that’s a minus.

If some one plays on your line and scores a goal that a plus if neither team scores then it’s a 0.

Finally banks and credit card unions use negative numbers

Negative numbers can be used to represent debits and positive to represent credits

It is easy to see how banks and credit cards use positive and negative integers to show weather money is deposited or withdrawn.

Case study weather of Indian cities

A better understanding of integer concepts is obtained by doing case studies.

Lets take an example of the weather of Indian cities .

We have taken two cities both which are situated below the sea level and compared the temperature of the cities of the year 2009.

The first city is Kargil which is 3048m below sea level.

The second is Delhi which is 239m below the sea level.

month Kargil (oC)

Delhi (oC)

January -4 21

February -2 24

March 5 29

April 14 36

May 21 40

June 26 29

July 30 35

August 29 34

September 25 34

October 19 34

November 10 28

December 1 23

Average temperature =sum of temperatures number of months Kargil : {(-4) +(- 2)+5+14+21+26+30+29+25

+19+10+1} ÷ 12 =14.125Delhi

(21+24+29+36+40+29+35+34+34+34+28+23) ÷ 12

=36.3333…

A man walks 75 km due north and then 9 km due south. Find his position with respect to his starting point ?

Solution:Let the starting point be zero.Let the movement towards north be

represented by a ‘+’ signThen let the movement towards south be

represented by a ‘-’ sign

Therefore 75km due north = +75 90km due south = -90 On adding we get, =+75+(-90) =75-90 = -15 Therefore his position with respect to

his starting point is 15km due south

AcknowledgementGroup 3 thanks Bhagya maam, for giving us the wonderful opportunity to help us make this PowerPoint presentation successful project thank you maam!