$\"\"$

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The circular helix is $\"\"$ .

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Show that the circular helix is a constant torsion and curvature.

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Consider $\"\"$ .

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Apply derivative on each side.

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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The curvature of the circular helix is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Therefore, the curvature of the circular helix is constant.

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$\"\"$

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The torsion of the circular helix is $\"\"$ .

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Substittute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Therefore, the torsion of the circular helix is constant.

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$\"\"$

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$\"\"$ and $\"\"$ .