Tag: history of mathematics

Let the capacity of cistern be $225$ units $\left (LCM\ of \dfrac {75}{2}\ and\ 45\right )$
$A$ does $= \dfrac {225}{75}\times 2 = 6\ units/ min$
$B$ does $= \dfrac {225}{45} = 5\ units/ min$.
Let pipe is turned off after $x$ minutes.
According to the question,
$6\times 30 + 5\times x = 225$
$5x = 225 - 180 = 45$
$x = 9$
After $9$ minutes, pipe $B$ is turned off.

Speed of train $A = 50\ kmph$
Speed of train $B = 60\ kmph$
Since, time is constant
$Speed \propto$ Distance covered
$\dfrac {S _{A}}{S _{B}} = \dfrac {D _{A}}{D _{B}}$
$\dfrac {50}{60} = \dfrac {D _{A}}{D _{B}}\Rightarrow \dfrac {5}{6} = \dfrac {D _{A}}{D _{B}}$
Given that train $B$ has travelled $120\ km$ extra.
$6x - 5x = 120$
$x = 120$
The distance between $A$ and $B = 6x + 5x = 11x$
$= 11\times 120 = 1320$
Alternate Method:
Let train $A$ start form station $A$ and $B$ from station $B$.
Let the trains $A$ and $B$ meet after/ hours.
$\therefore$ Distance covered by train $A$ in $t$ hours $= 50t$
Distance covered by train $B$ in $t$ hours $= 60t\ km$.
According to the question,
$60t - 50t = 120$
$\Rightarrow t = \dfrac {120}{10} = 12\ hours$.
$\therefore$ Distance $AB = 50\times 12 + 60 \times 12$
$= 600 + 720 = 1320\ km$.

 Bhaskaracharya composed the Siddhanta shiromany when he was $36$ years old.

Brahmagupta was an Indian mathematician and astronomer. He is the author of the Brahmasphuṭasiddhanta and the Khandakhadyaka.

Lilavati is based on Arithmetic. The book contains thirteen chapters, mainly definitions, arithmetical terms, interest computation, arithmetical & geometric progressions. Many of the methods in the book on computing numbers such as multiplications, squares & progressions

The bodhayan theorem is also called as Sulv theorem which later became known as Pythagorean Theorem.

In the 'History of mathematics' book, it is mentioned that Budhayana, the author of budhayana sulva-sutras, knew Pythagoras Theorem much before the birth of Pythagoras.

Pythagorean Theorem has been mentioned as a verse or a shloka in Baudhayana Sulbasutra. Here is the exact translation shloka in English:

Bhaskara work represents a significant contribution to mathematical and astronomical knowledge in the 12th century like the properties of zero, methods of multiplication, squaring, estimation of $\pi$ etc.

Bhaskaracharya was born in $1114 A.D.$ He represented the peaks of mathematical knowledge in the $12^{th}$ century and was the head of the astronomical observatory at Ujjain, the leading mathematical center of ancient India.