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You are not logged in. #1 20110422 23:18:26
Geogebra and jumping frogs.Hi;
Basically what you do is draw a unit circle around the origin. The origin represents the starting point of the frog. Draw another concentric circle with radius 2 (shaded circle). This represents all possible first jumps. WLOG pick a point on the shaded circle and call it B. Draw two tangents from B to the smaller circle. Call the tangent points F and G. Now it is just a geometry proof. Angle FBG is 60 degrees. The red circle represents all possible 2nd jumps. This angle of 60 degrees represents 1 / 6 of all possible second jumps. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 