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 “Aryabhattasiddhanta” 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.
1) What is the formula for finding area of a circle?
a) 2r
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
Sketch pens
Geometry box
glazed paper
A pair of scissors
Carbon paper
Adhesive fevicol
White chart paper


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

o
A
B

Form a crease joining BP and draw BP.
P
o
A
B

Arc AB subtends angle APB at the at the
point P and angle AOB at the centre O.
P
o
A
B

Make two replicas of angle APB using a
tracing paper or a carbon paper.
P
A
P
B
A
B

Now place these two replicas of angle
APB adjacent to each on angle AOB.
P
o
A
B

Repeat the above activity for the two
cases where arc AB is a major arc on or
a semicircular arc.
o
CASE – II
SEMICIRCULAR ARC
o
CASE – III
MAJOR ARC
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.
YOU
THANK