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

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SUMMARY

The discussion centers on calculating the diameter of the resulting circles when a circle with diameter X is twisted into a figure eight. Each approximate circle formed has half the circumference of the original circle, leading to a diameter that is half of the original diameter. It is important to note that while the total circumference remains constant, the total area of the two resulting circles does not equal the area of the original circle.

PREREQUISITES
  • Understanding of basic geometry concepts, including circumference and diameter.
  • Familiarity with the properties of circles and their transformations.
  • Knowledge of area calculations for geometric shapes.
  • Basic mathematical skills for manipulating equations.
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  • Research the mathematical properties of circles, including formulas for circumference and area.
  • Explore geometric transformations and their effects on dimensions.
  • Learn about the implications of shape changes on area and perimeter in geometry.
  • Investigate the concept of topology and how it relates to shapes like the figure eight.
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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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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:
 


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.
 

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