
Re: Trying to find perimeter of a regular pentagon
Posted:
May 28, 2013 9:50 PM


On 05/28/2013 09:04 PM, Ken Pledger wrote: > In article > <ea68917ec9a542feb4d79fbb0edcd10d@bz1g2000vbb.googlegroups.com>, > JT <jonas.thornvall@gmail.com> wrote: > >> On 28 Maj, 23:24, Ken Pledger <ken.pled...@vuw.ac.nz> wrote: >>> In article <425e7c8f10e6428fbcda44e1fbf8b850@googlegroups.com>, >>> .... >>> 260.sin(pi/5) or 260.sin(36 degrees).... >> >> I see your formula use Pi so i guess your formula can only calculate >> the perimeter to the precision of the given Pi and same would go for >> the area? > > > You're badly misunderstanding this. I used pi as the radian measure > of an angle, meaning the same thing as 180 degrees. That's why the > angle pi/5 may also be written as 36 degrees. >
[...]
This made me think of the origins of radian measure. Euler's formula says: exp(ix) = cos(x) + i sin(x), and obviously in that formula x is "in radians" ...
I know around the time of the French Revolution the French introduced "grad" = 1/100 of a right angle, so 360 degrees == 400 grad(s).
De Moivre came before Euler. With De Moivre's formula, cis(theta)^n = cis(n theta) there's no reason I see that theta has to be "in radians" ...
I might guess radians appeared very close to the time of Euler... (yet, maybe already calculus uses radian measure preferably, to get d/dx sin(x) = cos(x). )
David Bernier

