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I know what pi is used for and everything, but what exactly is it?
I know that it 180 degrees of a circle and everything like that, but what is it's significance, or how did they start to say "hey, we need to calculate this number to do such and such things."
this would help me better understand how to make certain programs.
Pi is the constant ratio between the circumference and the diameter of any circle.
a law is being debated in indiana as to how pi is 3.2
There's Indiana for you...
If you divide the circumference of any circle by its diameter, you get Pi. That is basically what it is. It isn't a rational number, hence why we get computers to calculate more and more digits of it. The more digits you have, the better you can estimate circumferences and areas based on knowing the circumference (or more usually the radius).
Because triangles can be considered as slices of a circle, and similar in 3D space, pi relates to angles in general. The degree system just divides a circle into 360 divisions - 360 because you can divide 360 by many whole numbers and still get a whole number. You can also say it contains 2pi radians, which is a more accurate description used in engineering and physics as it doesn't divide it up into 360 arbitrary units.
Why 2pi? Think about what pi is again. Given a diameter, multiply it by pi and you get the length of the circumference. Angles start from the centre of the circle and cycle round, so the length is the radius or 0.5 x the circumference. Therefore, to trace the path and get the length, you multiply it by 2pi instead. I had many lectures of it in my maths degree 7-8 years ago, but seeing as I don't use maths any more, the finer details have disappeared.
Now, can you explain why radians are more accurate than degrees?Quote:
Originally posted by andrewpolshaw
The degree system just divides a circle into 360 divisions - 360 because you can divide 360 by many whole numbers and still get a whole number. You can also say it contains 2pi radians, which is a more accurate description used in engineering and physics as it doesn't divide it up into 360 arbitrary units.
And why you claim a Degree is Arbitrary?
:)
Draw a circle whose radius is 1. (1 unit, doesn't matter what unit.)
Draw two radiuses (radii?) so that the length of the arc between them is 1.
The angle between the radiuses/radii is defined as "1 radian".
A little geometry shows there are 2pi radians in a circle.
The ancient Egyptians used base 60 for their arithmetic (much like we use base 10 today). For their own arithmetic convenience, they split the circle to 360 degrees. That's why it's arbitrary.
In mathematics, engineering, physics, you always work with radians. In real life, you usually use degrees.
(The difference between 10 and 20 degrees is more obvious than the difference between 0.17453292519943295769236907684886 and 0.34906585039886591538473815369772 radians.)
Yonatan has a basic concept of why we use 2pi as 360 degrees. If you guys remember the winding function thread a while back. That gives a thorough explanation as to what sin, cos, and radians have to do with anything. A reminder, the winding function is a circle with radius 1. Any point on the winding funtion is called (cos(a),sin(a)) where a is the angle of rotation from the x-axis going counter-clockwise. On the winding function, the angle of rotation is also equal to the arc length made by the angle of rotation, and notice that the circumference of the winding function is 2pi. So a complete rotation around the winding function is 2pi, 180 degrees is pi and etc.
Have fun!
degrees (so called babylonean religious unit) is less useful because it has no meaning other than the measurement of an angle.
Sure..Anyways bugz knows his stuff so i'll let him talk about stuff :P
Oh yeah, Babylonian, not Egyptian :o
andrewpolshaw said the following:
"Why 2pi? Think about what pi is again. Given a diameter, multiply it by pi and you get the length of the circumference. Angles start from the centre of the circle and cycle round, so the length is the radius or 0.5 x the circumference. Therefore, to trace the path and get the length, you multiply it by 2pi instead. "
However, it may be more accurate to say that we use 2*pi radians for the rotation around a circle, because the unit circle has a radius of 1, and the circumference would be 2*pi*r=2*pi in this case.
Btw, does anyone know the relationship between e, i, and pi?
:DCode:e^(i*pi)+1=0
In general:With the above formula (Euler's Formula) as a special case for x=pi.Code:e^(i*x)=cis(x)
e^((i*pi)+1)=0
or
e^(i*pi) + 1=0?
And what is cis?
e^(i*pi)+1=0
cis(t) is cos(t)+isin(t)
another relationship between e,i,pi
e*0=i*0=pi*0=0
so e*0+i*0+pi*0=0(e+i+pi)=0
this is Bugz's Formula :D
Nice bugz, you'll be the next Euler ;)
How does that work bugz? Is it not true that e^0=pi^0=i^0=1???
what do you mean? what are you talking about Kalk?
Actually, never mind...I'm being the slow person that I am...;)
e^0=pi^0=i^0=1 too
anything to the power of 0 = 1 :D
bugz is also correct, hardly a formula though :D
0^0=1?
00 = 0/0 which is undefined so 00 does not equal 1, it doesnt equal anything.
Your wrong. 0^0 and 0/0 are indeterminante. Not undefined.
Welcome Back A$$ Bandit, havent seen you here in a while? Wassup?
These guys have Pi to 1.24 trillion places. It took 5 years to design the prog which did the calc. They say having Pi to so many places serves no practical purppse regarding Pi itself, but improves scientific knowhow wrt calculations. Personally, I think they should chill a bit. Get day jobs.
By the way, you "only" need 49 digits of pi to calculate the circumference of the universe with an error of an atom's radius. :rolleyes:Quote:
Originally posted by Spooner
They say having Pi to so many places serves no practical purppse regarding Pi itself, but improves scientific knowhow wrt calculations.
That ought to be enough for anybody. Still, it is natural for scientists to want higher precision, and for mathematicians to want infinite precision.
They are undefined. Something like the exact value of pi, is indeterminable. There's a difference.
Actually 0^0 = 0/0 of a unit = "to" and "of" 1Quote:
Originally posted by A$$Bandit
00 = 0/0 which is undefined so 00 does not equal 1, it doesnt equal anything.
It is both 0 & 1.
Hence Indeterminate !
you guys are missing the point. infinity is not a numerical value, therefore you can't work algebra on it! and in the context of limits, 0/0, 0^0, inf/inf all of these sorts are indeterminate. values like 10/0 is not infinity, it is undefined (and you know why, from your own examples).
10/0 is not infinity, AND it is NOT undefined. 10/0 has infinite answers, therefore no answer is 100% correct or 100% incorrect.
undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined undefined
give me ONE answer to 10/0Quote:
Originally posted by blindlizard
10/0 has infinite answers
10 - - You have 10 apples, and divide them by 0 people. Each person gets 10
therefore 10*0=10 right?
10 apples per person, times 0 ppl, equals 10 apples!
If you have ten apples and they are sitting on a table, and you get zero people to come and eat them, they will remain forever sitting on the table. No one gets any apples!
Then you are saying 10/0 = 0. That is a possible answer
yes you are right, 0*0=10 also