Golden Ratio Exercises

: Math in Art: Golden Ratio Exercises
   By Ryan Mickelson on Saturday, January 31, 2009 - 02:04 pm: Edit Post

I found the following questions perplexing:

6. Where should we choose the point C on line segment AB so that the rectangle ABDE has the same area as the square ACFG? Justify your answer. {The answer is already given in figure 1.3.11. I'm not sure how to justify it.}

7. If the total length of the wire is 4236 ft., what is the base of the largest acute golden ttriangle that you can construct? {I do not understand how to subdivide this number.}

   By Sasho on Saturday, January 31, 2009 - 04:19 pm: Edit Post

6. Call AC=x, CB=y. The area of the square is then x2, while the area of the rectangle is (x+y)y. Equate these two and then solve for x/y.

7. The biggest such triangle should use all of the available wire. If the base of the rectangle is x, then its side is x*(phi), where phi is the golden ratio. Now solve x+2x*(phi)=4236, using phi=1.618.

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