Ring on a String
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The ring R is free to run along the taut string AB.
A second string passes through this ring and is pulled tight, before each end
is attached to a peg in the two lines of pegs.
Each line of pegs is perpendicular to AB, as shown in the diagram below.
Using a spreadsheet, determine the position taken by R as the positions of C and D vary.
You will have to make some decisions about start values for this investigation.
For example: how long will you make AB, and what different positions of C and D will you explore?
R will rest wherever the total distance DRC is a minimum.
Explore this as a practical activity on a home-made board.
Don't rush to see this, but when you are ready, there is a simple Excel file with an explanation, suggesting one way to use a spreadsheet to explore the Ring on a String problem.
There is also a second Excel file that uses extra techniques which assist presentation,
but the solution works the same way in either file.