Answer to Question #37672 in Geometry for amal

Question

Let x and y be any two points in a sphere (S^2). Let y' denote the antipodal point of y, then x,y and y' define a circle on a sphere. define a binary operation on S^2 such that x*y is the mid point of the arc joining x and y in the circle through x,y and y'.
My question is show that x*(y*z)=(x*y)*(x*z) for x,y and z belong to the sphere

Answer 1

Dear visitor
Unfortunately, the statement of your question is a bit confusing.
What is the definition of the sphere S^2? Please, give us the details so we could help you