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March 26, 2017

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The corners of the square, 2m. sides, are cut off to form a regular octagon. What is the length of the side of the resulting octagon?

  • geometry - ,

    Without loss of generality, assume a square of side 1. Now, if we cut off a piece of length x from each end of the side, then the diagonal of the cut corner will be x√2.

    To make things come out right, the two cuts and the remaining middle piece add up to 1:

    1 - 2x = x√2
    1 = (2+√2)x
    x = 1/(2+√2) = 1 - 1/√2 = 0.2928

    Check:
    1 - 2x = .4142
    .2928√2 = .4142

    So, I've solved for x. What is the side length?

  • geometry - ,

    Let x be the side of square and y be the side of octagon their for the relation between y and x is:
    y=x/1+2^1/2
    Theirfore y=.828

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