Projects And Homeworks of a school Student

 These are three activities on obtaining different conditions of solution for pair of linear equations in two variable. These are: To obtain the condition for no solutions of given pair of linear equation. T o obtain the condition for unique solutions of given pair of linear equation. To obtain the condition for no solutions of given pair of linear equation. Hope it helped you

Project on PI Hi This is a project on π-world's mysterious number.   

 Python program to calculate π Chundnovsky's formulae: `\frac{426880\sqrt{10005}}{\pi}=` `\sum _{k=0}^{\infty}\frac{(6k)!(13591409+545140134k)}{(3k)!(k!)^3(-640320)^{3k}}` import decimal  import math  #we use Chundnovsky's formulae def compute_pi(n):       decimal.getcontext().prec=n+1      A=426880*decimal.Decimal(10005).sqrt()      B=6      C=1      D=1      E=13591409      F=E      for i in range(1,n):           C=C*((1728*i*i*i)-(2592*i*i)+(1104*i)-120)/(i*i*i)           E+=545140134           D*=0-262537412640768000           F+=decimal.Decimal(C*E)/D      pi=A/F      return pi n=int(input("Enter decimal places:")) P=compute_pi(n) print(P)           if there is any mistake, please comment!

Euler's continued Fraction Formula: If `r_i` are complex numbers and `x` is defined by: ` x=1+\sum_{i=1}^{\infty}r_{1}r_{2}\cdot r_(i)=1+\sum_{i=1}^\infty  (\prod_{j=1}^{i}r_{j})` Then this equality can be proved by induction:  `x=\frac{1}{1-\frac{r_1}{1+r_1-\frac{r_2}{1+r_2-\frac{r_3}{1+r_3-\ddots}}}}` Its prove will be posted later...