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200902110226For this problem refer to Ladder vs Alley problem.
The following is a preliminary sketch of the “Ladders in Alley” problem which was introduced for me to solve by my good friend C. Blanco. My solution is not presented in a formal mathematical way. Also my notes are quite messy. Hopefully I will be able to describe my approach.
It is important to note that this work is incomplete and as such may have many errors.
There is a type of geometry known as inversive geometry. I am not familiar with the subject. However the important basis to this work deals with the fact that the circular arc has an inverse. Think of a mirror placed between the arc that is formed by the 4 meter ladder. We use the base of the ladder as the radius through which the ladder rotates.
There lies a radius which will intersects two points on the ladder. Here I doubled the radius from 4 to 8. But I don’t think it would matter what the mirrored length is as long as it is consistent between the two points.
Then it is just a matter of finding the length of the 4 meter ladder corresponds to the 1 meter height. I do not solve the complete problem here, since once this triangle is determined the problem is easily solved using trigonometry.
Review the Arched Doorway Problem
Click Here for 1st DXF file.
Click Here for 2nd DXF file.
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