Imagine a bicycle , wheel whose radius is one unit , with a marker attached to the rim of the rear wheel , as shown in the following figure . As the wheel rotates , the height h ( t ) of the marker above the center of the wheel , fluctuates between 1 and + 1 . The faster the wheel rotates , the faster the oscillation . Let us now choose our units of measurement so that the wheel has a radius of one unit . Then the circumference of the wheel ( the distance all around ) is known to be 2 , where π = 3.14159265 .... When the outer edge of the wheel has traveled this distance , it has gone through exactly one revolution , and so it is back where it started . Thus , if , at time t = 0 the marker started off at position h ( 0 ) = 0 , then it is back to zero after one revolution . If the cyclist happens to be moving at a speed of one unit per second , it will take the bicylce wheel 2 seconds to make one complete revolution , and so the wheel is back where it started atfer that time .