Accuracy of a statement

[jajrussel]

If I we're to state that the perimeter of a circle is always equal to or less than its area? If the argument (equal to) only appears once would this take away from the accuracy of the statement?

[michel123456]

The perimeter and the area have different units, and you cannot compare things that have different units. So I believe the statement is completely incorrect.

[jajrussel]

Thank you. I was trying to leave units out of the argument by not expressing units, well other than pi. Is the expression 12pi,or 144pi unacceptable as an answer when expressing perimeter or area?

 

Actually these numbers might not be the best way to say what I am asking. I'll try this way.

 

r equals 6

P equals 12pi

A equals 36pi

 

One more question since my keyboard does not supply the pi symbol do I need to imply multiplication as in 12×pi ?

Edited December 27, 2015 by jajrussel

[Strange]

The trouble is, area is inches squared or meters squared or whatever. And perimeter is just inches or meters. Depending on the units of measurement you use the area of a given circle could be a number that is greater or smaller than the number representing its perimeter.

 

For example, if the perimeter of the circle is 1 inch, then the area is about 0.08 square inches.

But the same circle has a perimeter of 25.4mm and an area of about 51 square mm.

[jajrussel]

The trouble is, area is inches squared or meters squared or whatever. And perimeter is just inches or meters. Depending on the units of measurement you use the area of a given circle could be a number that is greater or smaller than the number representing its perimeter.

 

For example, if the perimeter of the circle is 1 inch, then the area is about 0.08 square inches.

But the same circle has a perimeter of 25.4mm and an area of about 51 square mm.

Okay, thank you.

The reason I asked the original question is that I downloaded a program where you enter r, and it gives answers in expressions of pi. At first I found this to be annoying, because it forced me to get out another calculator to finish. However, even on my favorite calculator it will do the same thing, but it has an S to D key which finishes the translation, so to speak, and assumes that I will apply the correct units. Which I would hope to remember to do.

 

Though the output of the program was annoying to me it allowed me to see a pattern that I could use to replace my inability to remember the formulas for the perimeter and area of a circle.

 

I was trying to figure out how to write it down without being too confusing in the explanation. Maybe, I am being too meticulous.

[studiot]

You need to be careful here since your original premise is not even true numerically.

 

Consider the question

 

For what values of r is [math]2\pi r < \pi {r^2}[/math] ?

 

Set [math]2\pi r = \pi {r^2}[/math]

 

then [math]{r^2} - 2r = 0[/math]

[math]r\left( {r - 2} \right) = 0[/math]

 

r =0 or r = 2

 

For r<2 the statement is numerically incorrect anyway.

 

It is easy to see and test by substituting r=1 that the perimeter is going to be numerically greater than the area since 2 > 1.

Edited December 27, 2015 by studiot

[jajrussel]

Okay, scratch the statement. I wish I had thought to try 1 when testing the method I saw, when I saw the pattern the program shows. I could have skipped some embarrassment. Well, for maybe a day.

 

In my head the method would have said.

 

r=1

1+1=2 so, P=2pi

1×1=1 so, A=1pi, or simply pi

P>A, so statement is wrong.

 

Time to bang my head on the steering wheel. If the method I am using is easy enough to see with out me having to put my foot in my mouth trying to explain it, can you see any instances where the method will not work? I am no longer testing the accuracy of the statement. I do need to work on my math.

 

A couple more examples.

 

r=6

6+6=12, so P=12pi

6×6=36, so A=36pi

 

Or;

 

r=12

12+12=24, so P=24pi

12×12=144, so A=144pi

 

Thanks, by the way.

 

PS: studiot, I am still trying to figure out your test method. Many, many years ago when I was in school I actually liked algebra. Unfortunately the class ended before I learned anything. The test looks simular to what the teacher was trying to get me to do, while I was trying to think of other magic ways to make it work. All I learned is that my methods always came up short. Schools have a habit of letting you take a whole year over, but simply taking a class over just because you liked it resulted in one of those if you want to succeed you need need to consider other options speeches. I am old enough now to say that other options is probably not the best choice to force on anyone, at any age. I will figure out what you have written, but the younger me, that still lives along with the older me looks at it and says okay, it seems to make sense, but it looks like it could be easier. Anyway thanks again.

Edited December 28, 2015 by jajrussel

[studiot]

Those who made too much of units had a point, but went too far IMHO.

If your numbers had worked out, your statement could have been made too work with suitable adjustments, Instead of attacking the whole idea.

 

Consider the following (correct) statement.

 

There is always one more post than panel in a fence with no gaps or loose ends.

 

Two different units, but it is possible to compare the numbers.

 

[Manticore]

"Consider the following (correct) statement.

 

There is always one more post than panel in a fence with no gaps or loose ends."

 

Only if the ends of the fence are unconnected.

Edited March 6, 2017 by Manticore

[Bender]

Posts and panels aren't conventional dimensions but "number of something", which is in general dimensionless.

[Delta1212]

Those who made too much of units had a point, but went too far IMHO.

If your numbers had worked out, your statement could have been made too work with suitable adjustments, Instead of attacking the whole idea.

 

Consider the following (correct) statement.

 

There is always one more post than panel in a fence with no gaps or loose ends.

 

Two different units, but it is possible to compare the numbers.

 

Which is greater, 1 liter or 5 meters?

[studiot]

 

"Consider the following (correct) statement.

 

There is always one more post than panel in a fence with no gaps or loose ends."

 

Only if the ends of the fence are unconnected.

 

 

Well yes I agree I should have specified a straight run of fence, as one which forms a closed loop will have equal numbers.

 

O did not consider or include other fence constructions.

 

 

Posts and panels aren't conventional dimensions but "number of something", which is in general dimensionless.

 

Well you could try ordering "45 of something" from Jewsons and see if you get "The Jewson Lot"

 

 

See also my note below to Delta

 

 

Which is greater, 1 liter or 5 meters?

 

I don't think I ever said or implied that you could compare two amounts of any units indiscriminately.

 

In fact it is worth considering the reverse question:_

 

"Can two quantities with the same dimensions always be compared numerically?"

 

 

Well what setting on my torque - wrench do I require to exert a force of deliver 10 Joules? Edited

After all they have the same dimensions.

Edited March 7, 2017 by studiot

[DrKrettin]

 

Well you could try ordering "45 of something" from Jewsons and see if you get the "Jewson Lot"

 

 

 

Ha ha - which reminds me of a true incident when I ordered 200 fence posts from Jewsons. Because I needed to fence off a field on a steep slope, I specified 6' 6" lengths. When the delivery lorry came, knowing Jewsons, I carefully counted them, and counted 240. When I questioned it, the response was "ah yes - we didn't have any 6' 6", just 5' 6", so you have more." I asked whether I might have had 400 posts of 3' 3" instead, but they didn't get the point. They could not understand why I was not satisfied. This post doesn't have any point either.

[studiot]

 

 

Ha ha - which reminds me of a true incident when I ordered 200 fence posts from Jewsons. Because I needed to fence off a field on a steep slope, I specified 6' 6" lengths. When the delivery lorry came, knowing Jewsons, I carefully counted them, and counted 240. When I questioned it, the response was "ah yes - we didn't have any 6' 6", just 5' 6", so you have more." I asked whether I might have had 400 posts of 3' 3" instead, but they didn't get the point. They could not understand why I was not satisfied. This post doesn't have any point either.

 

Don't you put the longer posts at the bottom to keep the top of the fence level? +1

 

[Bender]

Obviously the correct unit for ordering posts is meter. Try ordering 400 m of posts next time, if only to see what they come up with.

 

Well what setting on my torque - wrench do I require to exert a force of deliver 10 Joules? Edited

After all they have the same dimensions.

It would be silly and confusing, but it would not be wrong . Except perhaps the terminology of "deliver", but my English is insufficient to make that call; in Dutch, it would work.

Edited March 8, 2017 by Bender