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# Speed Test for TI84 Calculators using a Pi-Calculator

To test the speed of your calculator, a special program has been written to calculate Pi using the Mclaurin series.It is known that atan(1) = π/4rad =45 deg. Further, it can be shown that the McLaurin series of :

atan(x)=x-(1/3)x^3+(1/5)x^5-(1/7)x^7+…….(1/(2N+1)x^(2N+1). For x=1 this results in :

atan(1)=1-(1/3)+(1/5)-(1/7)+…….(1/(2N+1) =π/4 which is transferred to the Ti-Basic program for Pi.

π=4*(1-(1/3)+(1/5)-(1/7)+…….(1/(2N+1))

Pi calculations are often used to test the speed of computers.

Program Picalc

Disp "Speed test Ti84 π-calculation with McLaurin series

Disp "π=4*(1-(1/3)+(1/5)-(1/7+.....1/(2N+1)

Disp "press enter"

Input "N=",N

­-1→M

1→P

For(J,1,N,1):

P+M/(2*J+1)→P         For loop

M*(­-1)→M

End

Disp "π=",4*P

Stop

For N = 10,000 runs, the calculated value for pi is 3.14169244, which is not an accurate value. The pi value used in the TI-84 calculators is 3.141592654. Furthermore, we conclude that the Ti-84 plus Ce is 2.5 times faster than the Ti-84 plus Silver Edition.

To achieve the same accuracy as the Pi value used in the Ti-84 calculators you need more than 100000 runs with this program.

Of course, there are algorithms that calculate Pi much faster way, but the intention here is to use the program for a speed test. 