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## #1 2011-04-22 23:18:26

bobbym

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### Geogebra and jumping frogs.

Hi;

Posted elsewhere is the problem of the jumping frog. Geogebra makes the problem easy and shows that it is more geometric than anything else.

A bullfrog leaps 2 meters in some direction. Does not like its location so it randomly leaps n meters again in some direction. If its odds of being within 1 meter from its original position are 1 / 6 then what is n?

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.

Line segments AB and BC are

long. That is the length of n.