Transcript from Piece of Pi - Home - Mrs. Burke's Math Page

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Aryabhata
Indian
mathematician
(476-550 AD)
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Aryabhata gave the following method for
determining pi:
“Add 4 to 100, multiply by 8, and add
again 62,000. The result is approximate
value of the circumference when the
diameter is twenty thousand.”
from Piece of Pi, by Naila Bokhari
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Do these calculations.
“Add 4 to 100, multiply by 8, and add
again 62,000. The result is approximate
value of the circumference when the
diameter is twenty thousand.”
What value of pi does this determination
yield?
from Piece of Pi, by Naila Bokhari
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(100  4)  8  62,000  62,832
from Piece of Pi, by Naila Bokhari
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(100  4)  8  62,000  62,832
62,832  20,000  3.1416
from Piece of Pi, by Naila Bokhari
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Aryabhata gave the following procedure
for finding the area of a circle:
“Half the circumference multiplied by
half the diameter is the area of a circle.”
from Piece of Pi, by Naila Bokhari
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Do the calculations for circles with the following dimensions. Use 3.1416 for .
C
1
C
2
d
31.416
10
12.56
4
75.3984
24
1
1
1
d A C d
2
2
2
A  r 2
from Piece of Pi, by Naila Bokhari
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Do the calculations for circles with the following dimensions. Use 3.1416 for .
1
1
1
d A C d
2
2
2
C
1
C
2
d
31.416
15.708
10
5
12.56
6.28
4
2
75.3984 37.6992 24
12
A  r 2
from Piece of Pi, by Naila Bokhari
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Do the calculations for circles with the following dimensions. Use 3.1416 for .
1
1
1
d A C d
2
2
2
C
1
C
2
d
31.416
15.708
10
5
78.54
78.54
12.56
6.28
4
2
12.56
12.5664
75.3984 37.6992 24
12
452.3904
452.3904
A  r 2
from Piece of Pi, by Naila Bokhari
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How accurate is Aryabhata’s rule?
Why?
from Piece of Pi, by Naila Bokhari
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How accurate is Aryabhata’s rule?
Why?
1
1
1
2
C d  2 r r   r
2
2
2
from Piece of Pi, by Naila Bokhari
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