Diameters in Terms of Radii

If d = 2r, then...

d^x ÷ 2^x = r^x

(In other words, the diameter of a circle to the power of any number divided by 2 to the same power equals the radius to the same power!)

Examples:

d = 6, r = 3

6^2 ÷ 2^2 = 36 ÷ 4 = 9 = 3^2

6^4 ÷ 2^4 = 1,296 ÷ 16 = 81 = 3^4


d = 10, r = 5

10^3 ÷ 2^3 = 1,000 ÷ 8 = 125 = 5^3


d = 24, r = 12

24^6 ÷ 2^6 = 191,102,976 ÷ 64 = 2,985,984 = 12^6


Even if x is negative, it still remains true!

d = 9, r = 4.5 (or 4½)

9^(-2) ÷ 2^(-2) = (1/81) ÷ (1/4) = 4/81 = (4.5)^(-2)

It's two(too) cool!

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© Derek Cumberbatch