Final answer:
The number 206265 is the number of arc seconds in one radian. One degree is divided into 60 arc minutes, which in turn is divided into 60 arc seconds, summing up to 3600 arc seconds per degree. Since there are 2π radians in a full circle, dividing the total arc seconds in a circle by 2π gives us the arc seconds per radian.
Step-by-step explanation:
The number 206265 corresponds to the number of arc seconds in one radian. When discussing minutes of arc (also called arc minutes) and seconds of arc (also called arc seconds), we're dealing with very small subdivisions of a degree. A degree is divided into 60 arc minutes, and each arc minute is further divided into 60 arc seconds. Therefore, 1 degree equals 3600 arc seconds (60 arc minutes * 60 arc seconds per arc minute).
When we talk about radians, the conversion is different. A full circle is 2π radians, equivalent to 360 degrees or 1296000 arc seconds (360 degrees * 3600 arc seconds per degree). To find out how many arc seconds are in one radian, we need to divide the total number of arc seconds in a full circle by the number of radians in a full circle, which is 2π radians. This leads to the following calculation: 1296000 arc seconds / 2π ≈ 206265 arc seconds per radian.