Geometric Construction: An Egg Shape
What Is an Egg Shape?
How would you describe the shape of an egg? Parts of it look like a circle, do you see that? But parts of it also look like an ellipse.
A geometric construction that results in the smooth curves of an egg, relies on one key concept.Look at the circle and ellipse.
Notice how they intersect at one point. This is a point that is tangent to each curve.
That means that if you connect a piece of the circle and a piece of the ellipse at this point, you get a smooth curve.
We will be using this idea to construct the egg shape.
Geometric Construction
The following construction can be done with a pencil, compass, ruler, and graph paper. You can also use geometry software to do this.
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Step 1 Construct segment AB. |
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Step 2 Construct the perpendicular bisector of AB and label it CD. Also, mark the intersection point. |
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Step 3 Construct a circle that has diameters AB and CD. |
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Step 4 Construct segments from points C and D that pass through point B. Make sure they extend beyond the circle. |
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Step 5 Construct the circle centered at point C that has radius of length CD. |
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Step 6 Construct the circle centered at point D that has the same radius as the other large circle. Mark Point E as shown. |
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Step 7 Construct the circle centered at point B that has radius of length BE. |
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Step 8 Highlight the arcs that define the egg shape. |
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