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Find out the general equation of sea shell type curvature.

I am a student of University of Dhaka, Faculty of Engineering and Technology. I have a problem to find out the combine equation of two curvature portion one is circular and another is parabolic. This type of geometrical shape is called sea shell type curvature and it is shown in my attachment JPEG file. If it is possible to find out the equation of this geometrical shape, please help me....

Re: Find out the general equation of sea shell type curvature.

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Originally Posted by

**siddiqueforum** I am a student of University of Dhaka, Faculty of Engineering and Technology. I have a problem to find out the combine equation of two curvature portion one is circular and another is parabolic. This type of geometrical shape is called sea shell type curvature and it is shown in my attachment JPEG file. If it is possible to find out the equation of this geometrical shape, please help me....

Why can't you write this as a hybrid function?

Re: Find out the general equation of sea shell type curvature.

Hello, siddiqueforum!

We can have a piecewise function.

. . $\displaystyle y \;=\;\begin{Bmatrix} \frac{x^2}{4} - f & \text{ if } x \le 0 \\ \\ -\sqrt{f^2-x^2} & \text{ if }x > 0 \end{array}$

They can be "combined", but it is still piecewise:

. . If $\displaystyle x \ne 0:\:y \;=\;\left(\frac{x-|x|}{2x}\right)\left(\frac{x^2}{4} - f\right) + \left(\frac{x+|x|}{2x}\right)\left(-\sqrt{f^2-x^2}\right) $

. . If $\displaystyle x = 0:\:y \,=\,-f$

Re: Find out the general equation of sea shell type curvature.

If you really, really, **want** to write it as a single formula, then you can write it as

$\displaystyle f(x)= \frac{1}{4f}x^2- f- (\sqrt{f^2- x^2}+ \frac{1}{4f}x^2)H(x)$

where H(x) is the "Heaviside step function".