c=dπ and a=πr^2
Easy enough for most right? Let's dig deeper.
This I do not understand.
If we have a radius of 2 inches, then c=dπ=4π and a=πr^2=4π
This makes c=a
Now lets do the same length in centimetres.
If we have a radius of 5.08cm(2in), then c=dπ=10.16π and a=πr^2=25.8064π
wait a second, in this case c≠a but 2in = 5.08cm
If we were to put this in practical use it seems like the area and diameter should always match. Say I take a piece of string. The length of it or diameter is always going to be the circumference if we were to turn it into a circle. One could argue the inside and outside of the string will have a different measurement depending on thickness but I'm referring to the measurement of the exact middle of the string.
I made what I called an rca comparison chart for some fun analysis. Please let me know if I made any errors anywhere.
If r=1 then c=2π a=π, r=2 c= 4π a=4π, r=3 c=6π a=9π, etc.
If we make a list of radii in whole numbers with the ratio of c to a it makes a pattern. Only the number 2 has an even ratio. 2 is the only whole number that is both positive and prime.
1 2:1
2 1:1
3 2:3
4 1:2
5 2:5
6 1:3
7 2:7
8 1:4
9 2:9
10 1:5
11 2:11
12 1:12
13 2:13
14 1:7
15 2:15
16 1:8
17 2:17
18 1:9
19 2:19
20 1:5
Now decimals, fractions, and irrational numbers
r=.5 or 1/2 c=π a=.25π
r=.25 or 1/4 c=.5π a=.0625π
r=1/3 c=2/3π a=π/9
r=2/3 c=1 1/3π a=4/9π
r=4/9 c=8/9π a=16/81π
r=5/9 c=1 1/9π a=25/81π
r=.2 or 1/5 c=.04π a=.04π c once again an even ratio
r=.02 or 1/50 c=.0004π a=.0004π another match
r=.002 or 1/500 c=.000004π a=.000004π the pattern repeats with the number 2
r=√2 c=2*√2π a=2π the square root of the radius is equal to the area times PI this time
r=√3 c=2*√3π a=3π another pattern
r=π c=2π^2 a=π^3
r=2π c=2π^3 a=4π^3
r=√π c=2π*√2 a=π^2
Does any of this make any cool patterns if graphed?
Easy enough for most right? Let's dig deeper.
This I do not understand.
If we have a radius of 2 inches, then c=dπ=4π and a=πr^2=4π
This makes c=a
Now lets do the same length in centimetres.
If we have a radius of 5.08cm(2in), then c=dπ=10.16π and a=πr^2=25.8064π
wait a second, in this case c≠a but 2in = 5.08cm
If we were to put this in practical use it seems like the area and diameter should always match. Say I take a piece of string. The length of it or diameter is always going to be the circumference if we were to turn it into a circle. One could argue the inside and outside of the string will have a different measurement depending on thickness but I'm referring to the measurement of the exact middle of the string.
I made what I called an rca comparison chart for some fun analysis. Please let me know if I made any errors anywhere.
If r=1 then c=2π a=π, r=2 c= 4π a=4π, r=3 c=6π a=9π, etc.
If we make a list of radii in whole numbers with the ratio of c to a it makes a pattern. Only the number 2 has an even ratio. 2 is the only whole number that is both positive and prime.
1 2:1
2 1:1
3 2:3
4 1:2
5 2:5
6 1:3
7 2:7
8 1:4
9 2:9
10 1:5
11 2:11
12 1:12
13 2:13
14 1:7
15 2:15
16 1:8
17 2:17
18 1:9
19 2:19
20 1:5
Now decimals, fractions, and irrational numbers
r=.5 or 1/2 c=π a=.25π
r=.25 or 1/4 c=.5π a=.0625π
r=1/3 c=2/3π a=π/9
r=2/3 c=1 1/3π a=4/9π
r=4/9 c=8/9π a=16/81π
r=5/9 c=1 1/9π a=25/81π
r=.2 or 1/5 c=.04π a=.04π c once again an even ratio
r=.02 or 1/50 c=.0004π a=.0004π another match
r=.002 or 1/500 c=.000004π a=.000004π the pattern repeats with the number 2
r=√2 c=2*√2π a=2π the square root of the radius is equal to the area times PI this time
r=√3 c=2*√3π a=3π another pattern
r=π c=2π^2 a=π^3
r=2π c=2π^3 a=4π^3
r=√π c=2π*√2 a=π^2
Does any of this make any cool patterns if graphed?