circle

i have a problem whit circles. i have a circle whit 5 in radius. in the circomferens i place 2 things that have a distance of 5. how do i calculate the angel between this 2 items? i know the circomferens is 2(pi)r. but how do you calculate the angel between 2 places in the circomferens if you only know the radius and the distance between them, the distance is squareroot((X1-X2)²+(Y1-Y2)²) just wanted to say this so u dont think the distance is around whit the circomferens

I'm sorry... I'm not sure I fully understand. Please type more carefully.

If I understand correctly, you want to know how to find the angle between two points, given the points and radius. You can easily find the circumference. You also know how to find the distance. Find both.

The ratio of the circumference and the distance is the same as the ratio between the degrees of a full circle and the angle in question. So, for distance = d, circumference = c, and angle = a:

d / c = a / 360

i said that the distance doesnt follow the circle. if you have 2 points on a circle and draw a straight line between them. then it wont follow the circle. thats the distance im talking about. the shortast way between both. it does not follow the circle. a friend said that i could use this formula c²=a²+b²-2ab cos C
and C is the angel between a and b, and a/b/c is sides of a triangel. but when i turn it around to get C free and type it on my calculator i get a imaginary number :confused: here is a link about that stuff http://hyperphysics.phy-astr.gsu.edu/hbase/lcos.html. can anyone of you guys try to get the C free?

I don't think I can explain this, but I can give an idea of what I think he is asking...

This will be your circle:


Excuse how the center isn't exactly the center...

You have a chord. A chord consist of a segment whose endpoints are on the the circle, the circle ebing any point equidistant from the center, in which your case is 5 units.


There is your radius.

Now, we need the chord.


You want to find the length of segment AB, correct? Is that what you are asking?

what im asking for is the angel A center B. that means if u draw and angel from A to the center and then a new one from the center to B we have an angel and its that one i want to know.

so you have the distance between A and B correct? that distance is called the chord

chord = 2Rsin(angle/2)

rearrange the formula and you get:

angle = 2(arcsin (chord/2R))

i don't know what grade you are in so i don't really know if you have learned this formula. I learned it in high school geometry, but didn't actually start using it until my sophmore year at college for my major.

but it's basic geometry

if you want, i can pm you a diagram

finaly, thanks alot, just a question, arcsin/sin^-1, are they the same, if they arent then why did you use arcsin in the formula when it shall be sin^-1?

tanks again for that formula daydreamer, now i have another question, if we have a shpere where the r = 10 and we are going to place points in the sphere, but also on the sphere. how many points do we get if the minimum distance between them is 5? how do u figure out that?

to figure out the amount of points on the sphere (on its area) ive used the area of a triangel. and then divide whit the area of the sphere. the area of a triangel whit X points and the points is equaly far away (distance = y) from each other can be written a=2,5(X-2)rot(y²-(y/2)²). for a triangel whit y=5 and x = 3 we get 10,82. x>2 that is a must. note that the triangels are next to each other and the area that is calculated is the total area of all of the triangel toghater.

a=y/2*(X-2)*rot(y²-(y/2)²)
x=2+a/(rot(y²-(y/2)²)*2,5)

and the sphere area is
a=4(pi)r²

and for out exempel wich had r=10
we get 4(pi)*10²=1257

2+1257/(rot(5²-2,5²)*2,5)=118 points on the sphere area. am i right or?

now to fill the inside of the sphere

now we take a pyramid whit triangel base and use the base we used before. but how to calculate the hight of the pyramid to make the side triangel indentical whit the base is the tricky part. for that we use the pythagoras again.

to make it simple lets put z=rot(y²-(y/2)²)
to calculate the hight we use h=rot(z²-(z/2)²)
why did i use that? i used the first z cause its the hypotenuse of the triangel we think on now. and the second z is half the way throught the base. then we reach the center. (just want to be sure you know how im thinking)
whit all this we get that h=3,75 exacly. so the pyramid is 3,75 high, and the base area is 10,825.

the volume of a pyramid is calculated 1/3ah, h is hight of the pyramid and a is base area. so the volume of this pyramid is then 1/3*3,75*10,825=13,53. and this is for 4 points and they are all 5 from each other. but how will it be if we add a new point? then we get 2 pyramids that is right next to each other. so whit X points and they are Y from each other we get this formulas to calculate the volume of the pyramids.
z=rot(y²-(y/2)²)
h=rot(z²-(z/2)²)
a=y/2*z
v=(X-3)ah/3

shouldnt it be then that we turn around volume formula so we get x free? then it should be like

x=3+3v/(ah)

and then we simply put in the volume of the sphere and we get the amount of points. or am i wrong?

yea, arcsin and sin^-1(x) are the same...i thought writing out arcsin would be clearer...i normally write out arcsin when i do homework so i dont get confused...

i left after i helped you with that formula...and i just got back (5 am...no sleep) so i'll look at that later in the morning...my brain probably wouldn't function too well right now because of the lack of sleep and physical exhaustion of swing dancing

ops i just discovered ive made a mistage. the stuff on the area of the sphere follow the sphere, which it shouldnt. the distance that follow the sphere should be slightly more. it should be:
angle = 2(arcsin (y/2r))
D=2(pi)r*angel/360
and then we should replace every Y whit tha D, this is for the X on the sphere area.
a=d/2*(X-2)*rot(d²-(d/2)²)
x=2+a/(rot(d²-(d/2)²)*0,5d)

D is about 5,23 when Y is 5. so if we put this in the formula we get:
2+1257/(rot(5,23²-(5,23/2)²)*5,23/2)=118

or am i wrong?
by the way, does anyone of you know a good site about Non-Euclidean geometry?