Yet another way of looking at why 1/2 might be imp. as a number for the critical line.................what is the def. feature of a circle?........any circle..........there are actually two defining features................a point and a radius.........but pi is about diameter...........................compared to the circumference............a diameter is twice a radius.............
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The number π (/ˈpaɪ/) is a mathematical constant, the ratio of a circle's circumference to its diameter. It is approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes spelled out as "pi".
https://en.wikipedia.org/wiki/Pi
https://www.khanacademy.org/...circumference.../circles-radius-dia...
Learn how the number Pi allows us to relate the radius, diameter, and circumference of a circle.
https://www.khanacademy.org/...circumference.../radius-diameter-circumference
Since circumference is 2 pi r, if I double the radius, I double the circumference or just multiply the original circle by the scale factor to get the next circle
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