Science And Mathematics In Sports _balbera_patiala

IN THIS PROJECT WE WILL HIGHLIGHT VARIOUS SIMPLE APPLICATIONS OF GEOMETRICAL FIGURES AND SIMILARITY IN THE DESIGNS OF VARIOUS SPORTS GROUNDS.

STUDENTS, LET US LEARN TO IDENTIFY SOME SIMPLE GEOMETRICAL FIGURES

EXPLAINING THE CONCEPT OF RECTANGLE

RECTANGLE IS A QUADRILATERAL WHOSE BOTH PAIR OF OPPOSITE SIDES ARE EQUAL AND EACH ANGLE IS 900

A

B

C

D

A RECTANGLE HAS BOTH PAIR OF OPPOSITE SIDES EQUAL. A

B

C

D

AB = CD

A

C

B

D

AC = BD

B

A 900

900

900

C

105

900 90

D

75

120 BETWEEN ANY TWO ANGLE 60 SIDES OF A RECTANGLE IS45900 135 150

65

180

∠BDC = 90

0

30

15 900 0

PAPER SHEET, CARD BOARD

STUDENTS SHOWING RECTANGULAR AND CIRULAR FACES ON DIFFERENT OBJECTS

STAMPS BUTTON SCALE PROTRACTOR(D)

STAMPS BUTTON SCALE PROTRACTOR(D)

FILTER PAPER

CONSTRUCT A RECTANGLE WHOSE SIDES ARE 3.4cm AND 2.7cm.

2.7cm

2.7cm

2.7cm

3.4cm 2

3

4

5

3.4 6

7

8

9

EXPLAINING THE TOPIC OF CIRCLES

P

S

O

R

Q

CIRCLE IS A GROUP (SET) OF POINTS WHICH ARE EQUIDISTANT FROM A FIXED POINT CALLED ‘CENTRE’.IN FIG;’O’ IS THE CENTRE.

P

S

r

r O

r

r R

Q

OP = OQ= OR =OS = r

‘r’ IS RADIUS

A

r

r O

DIAMETER=2r

B

S

O

P

R Q

1.HERE 4 POINTS ARE GIVEN. 2.‘P’ AND ‘S’ LIE ON THE CIRCLE 3.‘R’ LIES IN THE INTERIOR OF CIRCLE 4.‘Q’ LIES IN THE EXTERIOR OF THE CIRCLE

THE BOUNDARY OF CIRCLE IS CALLED ‘CIRCUMFERENCE’.

MEASURE THE RADIUS OF CIRCLE TO BE DRAWN FROM THE SCALE AS SHOWN.

1

2

3

4

5

6

7

8

9

0

NOW, DRAW THE CIRCLE

150

30

165

180

DIAMETER OF A CIRCLE DIVIDES A CIRCLE IN TO TWO EQUAL HALVES CALLED SEMI CIRCLES.

15 0

FOLDED FILTER PAPER

0 1 2 3

O

A

B

4 5 6 1

2

3

4

5

6

7

8

9

0

A

O

r

B

CENTRE OF

RADIUS OF

SEMI CIRCLE

SEMI CIRCLE

1 4

THE LAY OUT (map) OF VARIOUS COMMON SPORTS GROUNDS WERE SHOWN TO THE STUDENTS SUCH AS 1.BASKETBALL GROUND 2.FOOTBALL GROUND 3.CRICKET GROUND

FIGURES OR OBJECTS WHICH ARE SAME IN SHAPE BUT NOT IN SIZE ARE SIMILAR.

ALL CIRCLES, ALL SQUARES, ALL EQUILATERAL TRIANGLES ARE SIMILAR

•FIRST OF ALL STUDENTS CALCULATED THE DIMENSIONS OF THEIR LAY OUT (MAP) OF A SPORTS GROUND BY MAKING USE OF SCALE FACTOR •THEN THEY DREW THE LAY OUT (MAP) UNDER THE GUIDANCE OF MATH TEACHER S. PURAN SINGH

SCALE FACTOR IS A PROPORTIONAL CONSTANT ‘K’ WHICH HELPS IN DRAWING MAPS(LAY OUTS). FOR ENLARGEMENT OF A FIG; FOR REDUCTION OF A FIG;

×

LENGTH IN MAP = K (ACTUAL LENGTH)

SUPPOSE, WE ARE TO CONSTRUCT A RECTANGLE SIMILAR TO A GIVEN RECTANGLE SUCH THAT EACH SIDE OF THE REQUIRED RECTANGLE IS HALF THAT OF THE ORIGINAL RECTANGLE. SO IN THIS CASE

1 2

REDUCE THE DIMENSIONS OF A RECTANGLE ‘ABCD’ WHOSE SIDES ARE AB=9.6cm. AND BC=6cm. BY SCALE FACTOR OF 1

2

1 1 A′B ′ = AB = × 9.6 = 4.8cm. 2 2 1 1 B ′C ′ = BC = × 6 = 3cm. 2 2 where , A′B ′and B ′C ′are required

reduced

dimensions

STUDENTS WERE ASKED TO DRAW THE LAYOUT (MAP) OF THE SPORTS GROUND OF THEIR CHOICE BY MAKING USE OF SCALE FACTOR AND KNOWLEDGE OF CONSTRUCTION OF RECTANGLE ,SEMI CIRCLE, QUADRANT AND CIRCLES CLICK HERE TO SEE PROJECT

PROJECT COST : RS. 50 ONLY

1 25

1 50

ALTERNATIVE TO COMPASS; NAIL AND TIGHTENED ROPE

CRICKET PITCH

DRAWING CIRCLE WITH THE HELP OF A NAIL & TIGHTENED ROPE.

LAY OUT IS READY

LAY OUT MAP IS READY

PITCH

TEAM WITH COMPUTER FACULTY

TEAM WITH MATHS TEACHER S. PURAN SINGH

TEAM WITH MATHS TEACHER S. PURAN SINGH

ACTUAL DIMENSIONS

SCALE FACTOR 1 : 25

(15 m)

(6 .25 25 m cm )

(28 m)

112 cm ) m (5.8

60 cm

(3.6 m) 14.4 cm

(3.6 m)

m c 2 23.

14.4 cm

(1.25 m) 5 cm DIMENSIONS ON SCALE

ACTUAL DIMENSIONS

SCALE FACTOR 1 : 50

(20.12 m) 40.2 cm

(68.5m) (2 7. 4

m ) .8 54 cm

ON SCALE

137cm

WE ARE EXTEREMELY THANKFUL TO THE HEAD MISTRESS ,G. H. S.BALBERA FOR THEIR ABLE SUPPORT.WE ALSO EXPRESS OUR GRATITUDE TO MR.NARINDER KUMAR (CLUSTER COORDINATOR) FOR THEIR SINCERE EFFORTS IN MAKING THIS PROJECT A SUCCESS.