The circumference is divided into two equal parts based on point A at the 1st time.
Trisect the circumference in the 2nd time, quarter in the 3rd time and divide into 5 equal parts in the 4th time in the same way.
Points divided equally is being drawn on the circumference.
A figure below is the figure which drew the points that the circumference was divided equally up to the 5th time.
Answer the following questions.
(1) Find the number of points which overlap point B of the figure by dividing the circumference equally from the 3rd time up to the 50th time.
(2) Find the number of points added newly on the circumference at the 39th time.
Answer
(1) 16 pieces
Trisect the circumference in the 2nd time, quarter in the 3rd time and divide into 5 equal parts in the 4th time in the same way.
Points divided equally is being drawn on the circumference.
A figure below is the figure which drew the points that the circumference was divided equally up to the 5th time.
Answer the following questions.
(1) Find the number of points which overlap point B of the figure by dividing the circumference equally from the 3rd time up to the 50th time.
(2) Find the number of points added newly on the circumference at the 39th time.
Answer
(1) 16 pieces
(2) 16 pieces
Solution
(1) Point B is at the place of 1/3 clockwise based on point A on the circumference.
Solution
(1) Point B is at the place of 1/3 clockwise based on point A on the circumference.
The circumference is divided into 51 equal parts by the 50th time.
The points that overlap point B is the fractions which become 1/3 by reduction.
There are 16 fractions of 2/6, 3/9, 4/12, -----, 17/51.
(2) The circumference is divided into 40 equal parts at the 39th time.
The number of the points added newly on the circumference is equal to the number of the fractions whose denominator is 40 and which can't be reduced.
40 = 2 × 2 × 2 × 5.
The number to be found by subtracting the number of the multiple of 2 or 5 from 40 is the answer to be found.
40/2 = 20, 40/5 = 8, 40/10 = 4.
Thus 40 - (20 + 8 - 4) = 16.
