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(Convegence to fixed point) You were standing in the middle of a landscape holding a map...

(Convegence to fixed point)

You were standing in the middle of a landscape holding a map of the same area horizontally in front of you. Explain that there is one point on the map that is vertical to the corresponding point in landscape

Math   Calculus   
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Answer #1

Every point of the field has a one to one correspondance with the points in the map. Look at the following diagram. In the diagram a one to one correspondance is shown schematically. The map and the field is shwon. We strat from the top point and draw a straight line towards the map and extend it to the field. The two points where the line cuts the map and the field have one to one correspondance. Followig this map there will always be a point in the map that will be vertically connected with the corresponding point in the field. The point is shown here.

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