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In summary, the conversation discusses the possibility of deriving an approximate ratio between space and material in a ball wound with incompressible string. The string would be wound in a precise pattern to minimize space within the ball. The participants also discuss the possibility of using parametric equations and knot theory to plot the ball of string in 3D space. The ultimate goal is to fill 3D space with an expanding search path, similar to a spiral search in 2D.

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Would the string be randomly tangled, or wound in a precise pattern?

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Also, string is taut.

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For an Archimedes spiral it is easy but when I move to 3D I get lost.

I would like to plot my ball of string in matlab. I'm happy to plot the string as a space curve (I don't need to show the string's diameter,

Actually my real goal is to fill 3D space with an expanding search path. Akin to spiral search in 2D.

I'm hanramo a t ho tmail com

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Perhaps knot theory could help?

Space in a ball refers to the empty area inside the ball, whereas material refers to the matter that makes up the ball, such as the rubber or plastic used to create it.

Understanding the ratio between space and material in a ball can help in designing and manufacturing more efficient and durable balls. It can also aid in predicting the behavior and performance of the ball in different conditions.

There is no single formula to calculate the ratio between space and material in a ball as it depends on various factors such as the size, shape, and composition of the ball. However, it can be estimated by measuring the volume and surface area of the ball and comparing it to the amount of material used to make the ball.

Yes, the ratio between space and material can vary for different types of balls. For example, a basketball may have a higher ratio of space to material compared to a baseball due to the differences in their size and materials used.

The approximate ratio between space and material in a ball is not always precise as it depends on the measurement methods and assumptions made. However, it can provide a general understanding of the proportion of space and material in a ball.

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