Circle with diameter X and I twist the circle into a figure eight

In summary, twisting a circle into a figure eight does not change its diameter, circumference, or area. Since a circle is a two-dimensional shape, it does not have a volume to be affected by the twisting. Any circle, regardless of its diameter, can be twisted into a figure eight, although larger diameters may be more challenging to achieve a perfect shape. The flexibility of the material also plays a role in the ease of twisting.
  • #1
LitleBang
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If I had a circle with diameter X and I twist the circle into a figure eight how could I calculate the diameter of one of the resulting approximate circles?
 
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  • #2
Hi LitleBang! :wink:

Well, each approximate circle has half the circumference of the original circle,

and if the circumference is halved, then the diameter is … ? :smile:
 
  • #3


Notice that the total area of the two circles forming the figure 8 is NOT the same as the area of the original circle! But the total circumference is the same as the circumference of the original circle.
 

1. What happens to the diameter of the circle when it is twisted into a figure eight?

When a circle with diameter X is twisted into a figure eight, the diameter does not change. The length of the circle remains the same, but its shape is altered.

2. How does twisting a circle into a figure eight affect its circumference?

The circumference of the circle does not change when it is twisted into a figure eight. However, the path of the circumference changes as it goes through the figure eight shape.

3. What happens to the area of the circle when it is twisted into a figure eight?

The area of the circle does not change when it is twisted into a figure eight. The area of a circle is calculated using the formula A = πr², and since the radius remains the same, the area also remains the same.

4. Does twisting a circle into a figure eight change its volume?

A circle does not have volume, as it is a two-dimensional shape. Therefore, twisting it into a figure eight does not change its volume.

5. Can a circle with any diameter be twisted into a figure eight?

Yes, a circle with any diameter can be twisted into a figure eight. However, the larger the diameter, the more difficult it may be to twist it into a perfect figure eight shape. It also depends on the material of the circle and its flexibility.

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