How to apply mathematics to real world problems?

[uperkurk]

Let's say I see a parked car, the tire of the car is resting against the curb. Would you actually have to go with a tape measure and measure the curb, measure the wheel and then you'd be able to find the area underneath the curb and the tire?

It's just confusing. Soooo many math equations just use variables. But when it comes to the real thing, I'm confused.

 

[symbolipoint]

Let's say I see a parked car, the tire of the car is resting against the curb. Would you actually have to go with a tape measure and measure the curb, measure the wheel and then you'd be able to find the area underneath the curb and the tire?

It's just confusing. Soooo many math equations just use variables. But when it comes to the real thing, I'm confused.

EDIT: I missed seeing that the question had a very specific diagram, and so the "example" I posted is an area problem unrelated the uperkurk's question (and accompanying diagram).

?

Example:
An undetermined quantity of liquid material spilled. Estimate the area of the ground which the spilled material is covering, and calculate the length of absorbant roll material to cut in order to cover and absorb the spilled liquid material.

EDIT Again: My example seems more practical. The purpose of the area that the tire is covering of the curb is unclear, or at least seems not practicle. One could try to calculate or estimate this if he wanted.

 

[slider142]

Yes. The wheel is probably closest to an ellipse. Measuring the major and minor axes of the wheel will be enough to determine the ellipse, or any 3 points on the boundary if the major/minor axes are unclear. You will, of course, inherit the error bounds of your measuring rod. To be any more accurate, you would have to do a numerical integration: literally measure the height of the wheel over different partition types to find upper and lower bounds for the area, which is the best we can do for physical objects that are not abstract ideals.

 

[I like Serena]

What's your question?

Of course you can measure anything you want, but it helps if there's a real application.
There seems to be little point in calculating the area between curb and tire.
It becomes much more interesting if you try to calculate the area of rubber touching the road.
That may indicate for instance the distance it takes to brake to a stand still.

 

[uperkurk]

What's your question?

Of course you can measure anything you want, but it helps if there's a real application.
There seems to be little point in calculating the area between curb and tire.
It becomes much more interesting if you try to calculate the area of rubber touching the road.
That may indicate for instance the distance it takes to brake to a stand still.

Yeh that is something I didn't think of and probably would have been a better example. So how would one go about calculating the total surface area of the tire that is touching the curb

 

[I like Serena]

Yeh that is something I didn't think of and probably would have been a better example. So how would one go about calculating the total surface area of the tire that is touching the curb

Well, the area time the pressure in the tire should be equal to about a quarter of the weight of the car.