Math problem

Question

Start with a 90 degree angle. Then bisect both of the angles that you get. Then bisect them all again and again... How many times will you have to bisect the starting angle in order to finally end up with angles less than 0.1 degrees?

Answer 1

a_n = a₁(0.5)^n-1

0.1 = 90(0.5)^n-1

1/900 = 0.5^n-1

ln (1/900) = (n - 1) ln 0.5

ln 1 - ln 900 = (n - 1) ln 0.5

0 - 6.802 = (n - 1) (-0.693)

9.815 = n - 1

10.815 = n

 

You must cut 10 times.