Aryabhatta came to this

world on the 476 A.D at

Patliputra in Magadha

which is known as the

modern Patna in Bihar.

Some people were saying

that he was born in the

South of India mostly

Kerala. But it cannot be

disproved that he was not born in Patlipura and then

travelled to Magadha where he was educated and established

a coaching centre. His first name is “Arya” which is a South

Indian name and “Bhatt” or “Bhatta” a normal north Indian name

which could be seen among the trader people in India.

No matter where he could be originated

from, people cannot dispute that he

resided in Patliputra because he wrote

one of his popular “Aryabhatta-

siddhanta” but “Aryabhatiya” was

much more popular than the former.

This is the only work that Aryabhatta

do for his survival. His writing consists

of mathematical theory and astronomical theory which was viewed to be

perfect in modern mathematics. For example, it was written in his theory

that when you add 4 to 100 and multiply the result with 8, then add the

answer to 62,000 and divide it by 20000, the result will be the same thing

as the circumference with diameter twenty thousand. The calculation of

3.1416 is nearly the same with the true value of Pi which is 3.14159.

Aryabhatta’s strongest contribution was zero. Another aspect of

mathematics that he worked upon is arithemetic, algebra, quadratic

equations, trigonometry and sine table.

TO VERIFY THAT THE ANGLE SUBTENDED BY AN ARC AT THE CENTRE OF CIRCLE IS DOUBLE THE ANGLE SUBTENDED AT ANY POINT ON THE REMAINING PART OF THE CIRCLE. THIS PRESENTATION PROVES THIS THEOREM BY THE METHOD OF PAPER CUTTING, PASTING AND PAPER FOLDIND.

Basic terms related to

circle.

Meaning of angle

subtended by an arc. In

fig, O is the centre of the

circle and AB is the arc.

Arc AB subtends angle

AOB at the centre and

angle APB in the

remaining part of the

circle.

A

B

1) What is the formula for finding area of a circle?

a) 2r b) r

2) What is a radius?

a) A line segment from its centre to the perimeter.

b) A line segment joining the two points of the

circumference of the circle.

3) What is the centre of the circle?

a) Point inside the circle and is at an equal distance

from all of the points on its circumference.

b) Point anywhere in the circle.

4) What is a arc of a circle?

a) An arc is part of a circle's circumference.

b) An arc is a line outside the circle.

5) What is the angle subtended by an arc?

a) If the end points of an arc are joined to the centre of

a circle, then an angle is formed.

b) When the centre of the circle is joined to its

circumference.

• White chart paper

• Carbon paper / Tracing paper

• Geometry box

• A pair of scissors

• Coloured sheet of glazed paper

• Sketch pens

• Adhesive fevicol / gum

White chart paper

Carbon paper

Geometry box

A pair of scissors

glazed paper

Sketch pens

Adhesive fevicol

Cut a green glazed paper as a circle of

any radius with centre O.

Paste the cutout circle on white chart

paper.

A B

Mark the two points A and B on the

circle to have a minor arc AB.

A B

Form the crease by joining OA draw OA.

A B

Form a crease by joining OB and draw

OB.

A B

Mark a point P on the major arc i.e., the

remaining part of the circle.

Form a crease joining AP and draw AP.

P

A B

o

Form a crease joining BP and draw BP.

P

A B

o

Arc AB subtends angle APB at the at the

point P and angle AOB at the centre O.

P

A B

o

Make two replicas of angle APB using a

tracing paper or a carbon paper.

P P

A B A B

Now place these two replicas of angle

APB adjacent to each on angle AOB.

P

A B

o

Repeat the above activity for the two

cases where arc AB is a major arc on or

a semicircular arc.

CASE – II CASE – III

SEMICIRCULAR ARC MAJOR ARC

o o

From the above activity,

we observe that two

replicas of angle APB

completely cover angle

AOB.

Therefore, angle AOB =

2 angle APB.

Angle subtended by an arc at the

centre of a circle is double the

angle subtended by the same arc

at any other arc at any other point

on the remaining part of the

circle.

THANK

YOU