Example of a non-rectifiable closed jordan curve


Problems:

Example of a non-rectifiable closed Jordan curve.

Give an example of a non-rectifiable closed Jordan curve on the interval -1<=t<=1.

My thought: t + i(sin 1/t) + ?????

Please advise what curve I can add to make this work. Or, if this will not work, please provide an example of a non-rectifiable closed Jordan curve on -1<=t<1.

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Mathematics: Example of a non-rectifiable closed jordan curve
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