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start with a circle where the radius is length R heres an interesting question how many arcs of length R can we fit around the circle certainly one is not enough and we can see pretty quickly that two Arc lengths with a length of R is not enough how about three that looks like it could almost cover half we can check that 4 wont do the job and that 5 wont do the job either as theres still plenty of circle left over however when we try to cover this circle with six arcs of length R That Just About Does it and only leaves a little bit if we try with seven different arcs of radius R it covers the entire circle and theres overlap so we can fit six arcs of length R around the circle each such Arc of length R subtends an angle of one radian so this means that we can fit more than six radians in a circle in fact the total number two Pi of radians it fits in a circle is approximately 6.28