3. Indian mathematicians have made a
number of contributions to mathematics
that have significantly influenced
scientists and mathematicians in the
modern era. These include place-value
arithmetical notation, the ruler, the
concept of zero, and most importantly,
the Arabic-Hindu numerals
predominantly used today.
6. Aryabhata was born in Taregna, which is a small
town in Bihar, India, about 30 km from Patna
(then known as Pataliputra), the capital city of
Bihar State. Evidences justify his birth there. In
Taregna Aryabhata set up an Astronomical
Observatory in the Sun Temple 6th century.
There is no evidence that he was born outside
Patliputra and traveled to Magadha, the centre of
instruction, culture and knowledge for his studies
where he even set up a coaching institute. However,
early Buddhist texts describe Ashmakas as being
further south, in dakshinapath or the Deccan, while
other texts describe the Ashmakas as having
fought Alexander.
7. It is fairly certain that, at some point, he
went to Kusumapura for advanced
studies and that he lived there for
some time. A verse mentions that
Aryabhatta was the head of an
institution at Kusumapura, and,
because the university of Nalanda was
in Patliputra at the time and had an
astronomical observatory, it is
speculated that Aryabhata might have
been the head of the Nalanda
university as well. Aryabhata is also
reputed to have set up an observatory
at the Sun temple in Taregana, Bihar.
9. The Aryabhatta numeration is a system of
numerals based on Sanskrit phonemes. It
was introduced in the early 6th century by
Āryabhaṭa, in the first chapter titled Gītika
Padam of his Aryabhatiya. It attributes a
numerical value to each syllable of the form
consonant vowel possible in Sanskrit
phonology, from ka = 1 up to hau = 10
10.
11. In Aryabhatiya Aryabhata provided elegant results for the
summation of series of squares and cubes:
and
12. In Ganitapada 6, Aryabhata gives the area of a
triangle as
tribhujasya phalashariram samadalakoti
bhujardhasamvargah
that translates to: for a triangle, the result of a
perpendicular with the half-side is the area.
Aryabhata discussed the concept of sine in his
work by the name of ardha-jya. Literally, it means
"half-chord". For simplicity, people started calling it
jya. When Arabic writers translated his works from
Sanskrit into Arabic, they referred it as jiba
13. The place-value system, first seen in the
3rd century Bakhshali Manuscript, was
clearly in place in his work. While he did
not use a symbol for zero, the French
mathematician Georges Ifrah explains that
knowledge of zero was implicit in
Aryabhata's place-value system as a place
holder for the powers of ten
with null coefficients
However, Aryabhata did not use the Brahmi
numerals. Continuing the Sanskrit tradition
from Vedic times, he used letters of the
alphabet to denote numbers, expressing
quantities, such as the table of sine's in
a mnemonic form.
14. Mentalmaths questions
1) Express 1000 as a product of prime factor ?
➢ 23 x 53 = 1000.
2) Which prime numbers will be repeatedly
multiplied in prime factorizatation of 3200 ?
➢ 2.
3) Find the digit at units place of 8n if n is a
multiple of five ?
➢ 8.
4) What are the prime factors of denominators
of fraction 7/80 ?
➢ 7/24 x 5
15. 5) If HCF of two no is 68 & 85. what is the
LCM of two numbers ?
➢ 340.
6) What is the HCF of 95 & 152 ?
➢ 14.
7) Find the no which when divided by 18 gives
the quotient and reminder as 7 & 4?
➢ 130.
8) 176 when divided by a no gives the
reminder 5 & quotient 9 ? What is the
no?
➢ 19.
16. 9)By which smallest irrational number±27
be multiplied so as to get a rational
number ?
➢ should be multiply by ±3 to get a
rational no.
10) What is the product of (±7 + ±5)
and (±7-±5) ?
➢ 2.
