Approximation of a Circle's Circumference

[phi-lin good]

I've found a new way for finding the circumference of a circle by using a visual perspective ,an angle of 18 degrees, and law of sines, its formula is:

R is the radius of the circle
r is the new radius
C is the Circumference
h=17.7062683767
t=3.23606808139

(R/h)= r
(r/t)*360=C

with an error of 0.005079643% compared to C=pi*d because:
(180/(h*d))= 3.14143307999

3.14143307999/pi=.999949206146

example
R=6
6/h=.338863043999=r
(r/t)*360=37.6971969599=C
(pi*d)12*pi=37.6991118431

37.6971969599/37.6991118431=.999949206146

 

[robert Ihnot]

If we want to play around with figures, I guess we can get about anything we want.

In fact, this is sometimes done in the stock market with automatic programs, resulting in tremendous gains (in retrospection) with certain fudge factors based on yesterday's results. UNFORTUNATELY, the Market may not repeat itself. Or everyone could get very rich QUICK!

 

[HallsofIvy]

I've found a new way for finding the circumference of a circle by using a visual perspective ,an angle of 18 degrees, and law of sines, its formula is:

R is the radius of the circle
r is the new radius
C is the Circumference
h=17.7062683767
t=3.23606808139

(R/h)= r
(r/t)*360=C

I have no idea what you are talking about. Perhaps a picture would have helped. I assume that you have two circles of radius r and R- but why only one "circumference"? Are you saying you have two different circles with common center? What are "h" and "t" and how did you find those values. If you got h and t from trig functions, you are "begging the question". Those values are calculated from the presumed value of pi.

with an error of 0.005079643% compared to C=pi*d because:
(180/(h*d))= 3.14143307999

3.14143307999/pi=.999949206146

example
R=6
6/h=.338863043999=r
(r/t)*360=37.6971969599=C
(pi*d)12*pi=37.6991118431

37.6971969599/37.6991118431=.999949206146

 

[phi-lin good]

I used visual perception to calculate the circumference. Now I imagined if I walked a certain distance from the circle and measured its attributes from that distance and create a circle with these attributes, it will have a different radius and angle, but you can prove that the different attributes describe the same circle by mapping the dilation points of both circles. Taking this idea, I drew a circle (Circle A) and made an 18, 72, 90 right triangle with 18 degrees at the origin. At a certain distance 18 degrees can perceived as 1 degree. At this distance if you where to create a circle (Circle B) and measure its radius, the ratio of the radius of Circle A and Circle B is 17.7062683767 which equals h (h was just letter I picked). So if you divide the radius of Circle A by h, it will give you the radius of Circle B. Now in an 18, 72, 90 right triangle the length of the hypotenuse and the leg in the y-axis ratio is 3.23606808139 which equals t (again a letter I just picked). Since the hypotenuse equals the radius of the circle, the radius of Circle B divided by t represents the length of the leg corresponds to 18 degrees which also corresponds to 1 degree of Circle A and if you multiply the length by h, you will get the length that corresponds to 18 degrees of Circle A.

Using this information you can make a series of formulas

Circle A has a radius of R and Circle B has a radius of r
If r=R/h and h equals 17.7062683767

Then
r/t*360 ~ Circumference of Circle A
R*sin(1) ~ r*sin(18)
180/(t*h) ~ Pi
h*r*sin(18)~R*sin(18)
h*r*cos(18)~R*cos(18)

~ means approximation