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 2 years ago
Place four points on the surface of the sphere with radius 1m such that all four points are separated by equal distance from each other....
Find the distance between any two points.
 2 years ago
Place four points on the surface of the sphere with radius 1m such that all four points are separated by equal distance from each other.... Find the distance between any two points.

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hba
 2 years ago
Best ResponseYou've already chosen the best response.0@sauravshakya Do you have a diag ?

Kainui
 2 years ago
Best ResponseYou've already chosen the best response.2My intuition tells me that they will be separated such that they will form a regular tetrahedron by connecting the dots. When you say distance between any two points, do you mean in terms of traversing on the surface of the sphere or going straight between two points?

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.0traversing through the surface

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.0I mean on the surface

Kainui
 2 years ago
Best ResponseYou've already chosen the best response.2It might be difficult, but I suggest drawing a picture and finding out for yourself. The angles should be something like 109.5 degrees. At this point it's just finding the arc length by knowing that this ratio is always true \[\frac{ \theta }{ 2 \pi }=\frac{ arc length }{ 2 \pi r }\]

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.0But how did u get angle between any two point is 109.5 degree

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.0I got this question in the chemistry class

Kainui
 2 years ago
Best ResponseYou've already chosen the best response.2It's not very easy to draw out, but basically you have 4 arms coming outwards from the center and the angle between each one in 3 dimensions is 109.5 degrees. Only two are ever flat at one point. dw:1355919400604:dw

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.0I also know it is 109.5 degree but how to calculate it geometrically.

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.0I mean how to show the angle must be 109.5 degree

Kainui
 2 years ago
Best ResponseYou've already chosen the best response.2Alright let me work on it real quick.

Kainui
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1355920398348:dw cut diagonally on the cube with the tetrahedral angle in the center. dw:1355920471025:dw

Kainui
 2 years ago
Best ResponseYou've already chosen the best response.2Keep in mind, this is all pythagorean theorem up to this point, the sides of the cube all being 1 to keep things simple. The reason the diagonal through the center of the cube is sqrt(3) is because 1^2+(sqrt2)^2=3 because one edge of it is the hypotenuse of a triangle with legs of 1. Now let's look at what we can do here: dw:1355921319840:dw

Kainui
 2 years ago
Best ResponseYou've already chosen the best response.2I hope this explains it well, it's fairly difficult to draw out accurately without being a total piece of garbage.

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1i always wondered where that number 109.5... came from

Kainui
 2 years ago
Best ResponseYou've already chosen the best response.2I'm glad this could answer it! =D
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