Question

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.

Answer 1

@sauravshakya

Do you have a diag ?

Answer 2

My 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?

Answer 3

traversing through the surface

Answer 4

I mean on the surface

Answer 5

It 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

\[\frac{ \theta }{ 2 \pi }=\frac{ arc length }{ 2 \pi r }\]

Answer 6

But how did u get angle between any two point is 109.5 degree

Answer 7

I got this question in the chemistry class

Answer 8

It'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.

Answer 9

I also know it is 109.5 degree but how to calculate it geometrically.

Answer 10

I mean how to show the angle must be 109.5 degree

Answer 11

Alright let me work on it real quick.

Answer 12

cut diagonally on the cube with the tetrahedral angle in the center.