Geometry and location

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In summary, the conversation discusses the concept of precise location in mathematics and how it relates to real world objects such as the planet Jupiter. The question of whether the word "location" has a single mathematical definition is raised, and it is mentioned that in the case of Jupiter, there may be multiple locations or a single collection of points that define its position. The idea that the center of Jupiter exists at a single point while the planet itself exists at a set of points is also explored. This conversation ultimately highlights the complexity of defining location in both mathematical and real-world terms.
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Eh

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A precise location is defined as a point with zero dimensions. So we can easily tell you where the location of something is, say at (x,y,z) from the starting point. But let's say you had a map of the solar system, and used a scale that is too small. The planet Jupiter would now be found at several locations at once.

Anyway, the question is: does the word "location" only have one mathematical definition, being an exact point? In the case of Jupiter, are there there several locations where you will find the gas giant, or can you define a single location as a collection of points?
 
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Most people would be happy with the definition that the center of the planet exists at a single point in space, while the planet itself exists at a set of points.

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"Point" is, as you say, a mathematical concept. "Jupiter" is NOT a mathematical concept. You could, of course, set up a mathematical model that more or less accurately modeled Jupiter. Whether you could assign a single point to Jupiter would depend upon your mathematical model.
 

What is geometry?

Geometry is a branch of mathematics that deals with the study of shapes, sizes, relative positions of figures, and the properties of space.

What are the basic elements of geometry?

The basic elements of geometry include points, lines, angles, surfaces, and solids. These elements are used to define and describe shapes and their properties.

What is the difference between Euclidean and non-Euclidean geometry?

Euclidean geometry is the study of flat or two-dimensional surfaces, while non-Euclidean geometry is the study of curved or higher-dimensional surfaces. Non-Euclidean geometry also includes different axioms and postulates than Euclidean geometry.

What is the importance of geometry in real life?

Geometry is used in many real-life applications, such as architecture, engineering, navigation, and art. It helps us understand and describe the world around us and make accurate measurements and calculations.

How is geometry related to location?

Geometry and location are closely related as geometry is used to describe and determine the position of objects in space. It also helps us understand the concept of distance, direction, and orientation, which are essential in determining location.

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