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# Quarter Circle Arc Ellipse Approximation

In manufacturing and design it is often easier to create ellipse approximations rather than true ellipses. Several methods of creating pseudo-ellipses use circular arcs.

For example, two pairs of quarter circle arcs can be used to make a figure that looks very much like a true ellipse. The size difference between the arcs determines the shape's eccentricity.

Denote the length of the half-major axis by

*, the half-minor axis by*

**a***, the longer arc radius by*

**b***, and the shorter arc radius by*

**r**_{2}*. If you know both*

**r**_{1}*and*

**a***, then you can determine*

**b***and*

**r**_{2}*.*

**r**_{1}Likewise, if you know

*and*

**r**_{2}*, you can solve for*

**r**_{1}*and*

**a***. All of the necessary formulas are given below, or you can use the convenient calculator above.*

**b**### Calculating *r*_{2} and *r*_{1} from *a* and *b*

Given dimensions _{2}

_{1}

*a*and

*b*, where

*a*≥

*b*and

*a*≤ (1+√2)

*b*, you can find the values of

*r*and

_{2}*r*as well as the perimeter and area with the equations

_{1}### Calculating *a* and *b* from *r*_{2} and *r*_{1}

Given _{2}

_{1}

*r*and

_{2}*r*, you can find the values of

_{1}*a*and

*b*as well as the perimeter and area with the equations

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