| The Shape of Footballs |
| Each of the four footballs below has a slightly different cross-sectional shape. We can recreate that shape by intersecting two ellipses. |
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| American football |
Australian Rules football |
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| Rugby League football |
Rugby Union football |
| In the window below are two circles separated by a small distance, with the intersection of the two circles producing the red outline. Rotating that outline through 180° produces the 3D object to the right. Grab the object with your mouse and drag it about for an all over look. |
| Now use the sliders to change the values of x0 and b. Changing the value of b will modify the circles into ellipses (short and fat or long and thin), and changing the value of x0 will move them further apart or closer together. |
| What values of x0 and b produce the four football shapes? How about a soccer ball, a discus, or a spear? |
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| Can any of your shapes be called an 'oblate spheroid' or 'prolate spheroid'? |
