Seeking help with visualizing surface

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SUMMARY

This discussion centers on the concept of visualizing the relationship between two variables, x and y, in terms of their respective units of measurement. The user explores the implications of having different "sizes of 1" for each variable, suggesting scenarios where the unit for x is 1 while the unit for y is slightly less, and vice versa. The conversation highlights real-world examples, such as aircraft height in feet versus horizontal distance in miles, and the varying lengths of degrees of latitude and longitude. The need for mathematical insight is emphasized, particularly in understanding these relationships.

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  • Understanding of basic mathematical functions and variables
  • Familiarity with units of measurement and their applications
  • Knowledge of coordinate systems and geographical measurements
  • Basic concepts of dimensional analysis
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Kmenex
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I'm a rogue babble master, hear me out.

I have been puzzled by this little idea concerning functions and the "relation" between the "size of the 1" for, say variable x, and the "size of the 1" for variable y. Naturally the two variables x and y both take "the unit" as their size of 1, and this unit has the same size in both x and y. Don't even let me mention my nonsense about "distinct sets of real numbers"

Well, what would happen if this were not the case? What would happen if the "size of 1" in the y direction was not the same as the size of 1 in the x direction? I like to describe this by saying that when x's unit = 1 then y's unit = .99998 (or something), and when y's unit = 1 then x's unit = 1.00002 ...

And then what happens when you let the difference between the units change as a function of x, or...

hmmm this isn't very well thought out.. maybe a mathematician can help me.
 
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Hi Kmenex! :smile:

We do this quite often.

For example, an aircraft measures its height in feet, but its horizontal distance in miles … that doesn't create any problems!

And degrees of laitude and longitude are of different lengths (except at the equator), and the ratio depends on where you are! :smile:
 

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