The functions of curve lines

[apprenticeLv5]

If I draw curve lines on a paper randomly, could all of those be represented in functions?

 

[Deleted member 4993]

If I draw curve lines on a paper randomly, could all of those be represented in functions?

No ! Those have to pass vertical line test.

 

[Dr.Peterson]

If I draw curve lines on a paper randomly, could all of those be represented in functions?

That depends on what sort of function you have in mind.

In general, it won't be y = f(x); but it could be a parametric function, x = f(t), y = g(t) for 0 <= t <= 1.

 

[apprenticeLv5]

No ! Those have to pass vertical line test.

Thank you for your answer. That test looks useful to solve my question.

 

[apprenticeLv5]

That depends on what sort of function you have in mind.

In general, it won't be y = f(x); but it could be a parametric function, x = f(t), y = g(t) for 0 <= t <= 1.

Thank you for your answer. It's clear to me now. That was exactly the one in mind.

 

[YourNerdiness]

I remember seeing something one time about this, and I'm pretty sure that yes, random scribbles on paper can be graphed, but unfortunately, I cannot find the video now.

 

[apprenticeLv5]

I remember seeing something one time about this, and I'm pretty sure that yes, random scribbles on paper can be graphed, but unfortunately, I cannot find the video now.

That's a shame. I wanted to check the video too.

 

[Dr.Peterson]

random scribbles on paper can be graphed

A random scribble already is a graph, in the sense of a set of points on the plane!

The problem is, you can't generally find an accurate formula for the (parametric) function whose graph it is.

 

[chrislav]

thats why topographers
cannot find exacktly the area of any property which at least has a curved line in its perimeter

 

[Otis]

cannot find exacktly the area of any property which at least has a curved line in its perimeter

I understand what you have in mind, chrislav, but I wouldn't say "any" such property because there are exceptions (eg: circular arc connecting opposite corners of a square lot).

 

[chrislav]

I understand what you have in mind, chrislav, but I wouldn't say "any" such property because there are exceptions (eg: circular arc connecting opposite corners of a square lot).

yes you can constract a property of that shape and you can find exactly the area ,but for existing properties this is very rare or nearly impossible
because for existing properties you have to find out first the shape of your property which practicaly speaking no topographer will take the task to do so because the time needed is extremely big

 

[Otis]

for existing properties this is very rare

Ah, but chrislav, I'm thinking as a mathematician (albeit, not an economist). The fact that such properties exist makes them exceptions to the meaning of 'any'.

 

[chrislav]

According to the laws of logic yes