Counting squares...

[YouAreNowReadingMyName]

This sounds ridiculous but...how do we count squares efficiently?!! Whenever it's a curved graph like in gravitational potential energy changes in space I spend ~15 mins trying to count them. This is an incredibly frustrating part for me because a) I think it's a ridiculous part of the course and b) I waste so much time on it...

[lzxnl]

This sounds ridiculous but...how do we count squares efficiently?!! Whenever it's a curved graph like in gravitational potential energy changes in space I spend ~15 mins trying to count them. This is an incredibly frustrating part for me because a) I think it's a ridiculous part of the course and b) I waste so much time on it...

I cannot agree with this more. I really can't. Just let people find out areas using maths, instead of vague and inaccurate area estimates.

Mark each square counted by dotting it with your pencil and for the curved ones, just estimate.

And if you "have a feeling" that you're missing one or two squares then add 1 or 2 onto what you've counted.

They're pretty lenient with the curved counting graph squares though; from what I've heard there's a range of like up to 10 squares you can be within (depending on the graph of course).

See, vague. Accuracy isn't even needed. Generally the uncertainty is pretty huge, like around 10-20% of the final value.

[YouAreNowReadingMyName]

Ok, thanks, but, any tips on speed of counting?

[~T]

I turn everything into a few trapeziums that cover approximately the same area (literally draw over the top of the graph)

This seems to be more accurate for me. Then you just use the trapezium area formula for each that you've drawn (average height multiplied by width)

[SocialRhubarb]

Trapezium method is definitely valid for most graphs. Unless your curve is really wonky, I'd recommend using trapeziums, like Tim...blahhh's suggested.

Alternatively, my friend does the integration on a separate paper, writes 'calculate area under the graph by counting squares' at the top of his actual page, and just happens to use the exact right number of squares each time.

Amazing.

[Robert123]

One method that I was reccomended to use when counting squares is to actually number them instead of just dotting. This allow you to easily check back on them to see if you made a mistake or not

[lzxnl]

One method that I was reccomended to use when counting squares is to actually number them instead of just dotting. This allow you to easily check back on them to see if you made a mistake or not

Highly recommended, I do that all the time.

For the cases where you have a really flat curve, like for gravitational field strength, trapeziums are really fast. However, make sure you do actually draw some trapeziums that approximate the area well.

Trapezium method is definitely valid for most graphs. Unless your curve is really wonky, I'd recommend using trapeziums, like Tim...blahhh's suggested.

Alternatively, my friend does the integration on a separate paper, writes 'calculate area under the graph by counting squares' at the top of his actual page, and just happens to use the exact right number of squares each time.

Amazing.

[monty]

colin hopkins said to count any square with more than half shown and disregard all the other squares with less than half of them shown.. thats how i have been tackling it as well.