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Good link, TFF.
I could with that sort of explatation for the more complex stuff.


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Bill, is there anything specific that you're looking for?

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Quote:
Bill, is there anything specific that you're looking for?


There is a hole in my education where the basis of maths should be. As a result, any efforts I make to master the practicalities are hampered by lack of foundations.

You will appreciate that this is an impediment to grasping scientific concepts, especially in view of my advancing years. Learning is a lot slower process than it was, so I don't kid myself that I shall master calculus, but anything that helps to move in that general direction is a bonus.


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paul Offline OP
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Quote:
Would I be spoiling an academic discussion if I were to ask what, in the real world (whatever that is), is the distinction between: a banana and a banana^2?


1 banana = 1 banana

if a banana is 1 banana in lenght then
1 banana * 1 banana = 1 banana squared.
or
1 banana * 1 banana = 1 square banana.

if you are using meters as the length then you would have

when calculating area
1 meter * 1 meter = 1 meters squared

and

2 meters * 2 meters = 2 meters squared

and

3 meters * 3 meters = 3 meters squared

or

1 meter * 1 meter = 1 square meters

and

2 meters * 2 meters = 4 square meters

and

3 meters * 3 meters = 9 square meters


we have no symbol to use for square meters so TFF used
the ^2 which is not correct and he wrote his answer out
as four bananas squared when he solved his equation!!!

2 bananas * 2 bananas = 4bananas^2 (four bananas squared)

he should have used
four square bananas
or
two bananas squared

that is what this is about.

I know its confusing but the confusion comes from the lack of a symbol to use when writing out a formula or a result of a formula.

it was when he wrote out what his result meant that I realized he thought that squared was the same as square.















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Thanks, TFF.

Duty calls, but I'll have a look at those links a bit later.


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A banana is not "one banana" in length, because "banana" is not a length. (We could define a banana as some arbitrary length, but we would need to remember that real bananas are generally not the same standard length.)

Usually, the length of a particular banana will be in a standard unit of length.

We would not compute the total length of a bunch of bananas by multiplying bananas by bananas, even if we do use the "banana" as a standard unit of length.

Paul wrote: "it was when he wrote out what his result meant that I realized he thought that squared was the same as square."

I'm still not convinced I'm wrong on that. I only said that I might be wrong - and I still think that I *might* be wrong. Certainly Dr Math disagrees with me and I acknowledge he knows a lot more about it than I do.

I don't have a problem - none at all - with being wrong. My problem is one of consistency.

Regardless of what anyone thinks: 4m^2 is equivalent to a 2x2 grid, with each cell being a 1mx1m.

We read this as "four meters squared" in normal discussion in the same way that we might read
4m^3 as 4 meters cubed and
4m^5 as 4 meters to the fifth

That is, in normal mathematical notation, the exponent ONLY applies to the presenting element (in this case, the 'm').

If Dr. Math (and Paul) are correct in that
"4 meters squared" actually means (4 meters)^2 = 16 square meters

then you have a case where this regular case means something different than what we normally mean when we use mathematical notation (and MOST technical people use the technical notation).

I don't have a problem with common usage being different than technical usage. If that were the issue, then this is not worth discussing. But Dr. Math did not give any indication that this was "just the way lay people talk about it."

On the other hand, wolfram alpha agrees with me, which is odd, because ostensibly, I thought they were the same group of people behind both of them.

I have sent an email to request clarification. He has responded to me quickly on two previous occasions relating to other matters, but I have not gotten a response on this yet. I'm not complaining; merely noting. The guy probably gets hundreds of emails daily; he can't answer them all.

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paul Offline OP
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Quote:
We would not compute the total length of a bunch of bananas by multiplying bananas by bananas, even if we do use the "banana" as a standard unit of length.

Paul wrote: "it was when he wrote out what his result meant that I realized he thought that squared was the same as square."


then why did you write your answer to your equation the way you did?
2 bananas * 2 bananas = 4 bananas ^2 (four bananas squared)

the way you wrote your answer is sudgesting that bananas have a length?

if bananas dont have a length then why wasnt your answer

simply 4 bananas

why did you write

4 bananas^2 (four bananas squared)



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paul Offline OP
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Quote:
Regardless of what anyone thinks: 4m^2 is equivalent to a 2x2 grid, with each cell being a 1mx1m.


no , a 4x4 grid = 4M^2 with each cell being a 1mx1m.

a 2X2 grid = 2 squared not 4 squared

4 meter length * 4 meter length = 16 square meters

2 meter length * 2 meter length = 4 square meters

2 meter length * 2 meter length = 2 meters squared







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paul Offline OP
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Quote:
then you have a case where this regular case means something different than what we normally mean when we use mathematical notation (and MOST technical people use the technical notation).


YES

thus the dangers of not having a square symbol and the necessity of this discussion in its own discussion.




we shouldnt use ^2 for both square and squared

because 4^2 and 4^2 look the same

but 4 square and 4 squared are different

these would work


254 np ■

223 np ▀

8 np ◘

but they wont work in this forum

what we really need on this forum is a smiley for square mad
4 mad ft * 4 madft = 16 mad ft














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Originally Posted By: paul

then why did you write your answer to your equation the way you did?
2 bananas * 2 bananas = 4 bananas ^2 (four bananas squared)

the way you wrote your answer is sudgesting that bananas have a length?

if bananas dont have a length then why wasnt your answer

simply 4 bananas

why did you write

4 bananas^2 (four bananas squared)



Writing:
2 bananas * 2 bananas = 4 bananas ^2 (four bananas squared)

IF a "banana" is a unit of length then "bananas squared" would be a unit of area. (I'm not saying that bananas are standard units of length - I'm positing a hypothetical.)

2ft * 2ft = 4ft^2

length * length = area

Suppose I had a "standard banana" and I wanted to find the length of my office in standard bananas.

I count 15 across.

The equation is not
Length of office= 15 bananas * 1 banana

The equation is
Length of office= 15 * 1 banana

If I wanted to know the AREA of my office, suppose it is 15 bananas in one direction and 20 bananas in the other direction. The formula would be:

Area of office = 15 bananas * 20 bananas = 300 bananas^2

(The square ONLY being applied to the bananas and NOT to the 300.)

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paul Offline OP
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Quote:
2ft * 2ft = 4ft^2


write that out

use the mad smiley for square

ie...

4 madft

or

4 ft mad

both the above have the same value.







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2ft * 2ft = 4ft^2

Two feet times two feet equals four feet squared.

I could also write it as:
Two feet times two feet equals four square feet.

According to Dr. Math (and you) these mean different things. I don't recall ever having heard a single technical person using these as anything other than synonyms.

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paul Offline OP
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Quote:
Two feet times two feet equals four feet squared.


I will use the mad for 1 sq ft

mad mad mad mad
mad mad mad mad
mad mad mad mad
mad mad mad mad

notice there are 16 square feet in 4 feet squared

the above is 4 feet SQUARED you can tell by counting
the number of linear feet on each side of the SQUARE

the below is 2 feet SQUARED you can tell by counting
the number of linear feet on each side of the SQUARE

mad mad
mad mad

notice there are 4 square feet in 2 feet squared


see the difference?

lets check this

the below is 1 foot SQUARED you can tell by counting
the number of linear feet on each side of the SQUARE

mad

notice there is 1 square foot in 1 foot squared



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Bill S. Another good source to learn about math is The Khan Academy. There is a lot of stuff in there. The mathematics section starts at a simple level and builds on up through Calculus and Linear Algebra. You should be able to find something
at any level you need there.

So try the Fiends links and mine. You should be able to find something that will help you.

I may be running a bit late getting back to you, but Turner Classic Movies had a Buster Keaton festival a few days ago and I am still working my way through the ones I recorded. I just finished "The Navigator". Anybody who is interested should be aware that Buster Keaton was one of the funniest comedians in the movies, and they are still just as funny as when he made them.

Bill Gill


C is not the speed of light in a vacuum.
C is the universal speed limit.
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I see the difference. I have never seen it mean that previously. This would be inconsistent with every other technical expression.

In writing the notation 4ft^2, every technical person would recognize the latter, 2x2 grid (or equivalent).

If Dr. Math is correct, then when speaking the words, we would have to be inconsistent with every other technical expression.

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paul Offline OP
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thats why we need a symbol for square because communication between several tech's could result in big problems.

if it already hasnt.

ie..

one tech calls another to ask how large of an area something is.

his worded reply was four square feet , the caller writes down 4ft^2

and orders enough steel to cover 16 square feet.


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It's possible, though I've never heard it used that way.

*USUALLY* we are at a whiteboard and we write down the notation or we are sending emails where we also use the notation.

There are occasional cases where someone is talking and I don't know what they're driving at, so I ask them to write it down. I can't think of any examples at the moment, but I'm pretty sure this is not among them. It's extremely infrequent, because usually we're talking in front of the formulae where there is no ambiguity.

I have not seen kallog weigh in on this. I'm curious to know whether he has ever heard or seen it used as
4 meters squared means (4 meters)^2 instead of 4 (meters^2)

Ah...I can think of one case, actually. The term Kilobit means something different to communications engineers and computer designers or system admins. Kb to a comm engineer means 1000 bits; Kb to a system administrator means 1024 bits. I'm not saying there aren't some inconsistencies in terminology between fields, but I have never known the interpretation of "squared" to be among them.

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Originally Posted By: Bill
Bill S. Another good source to learn about math is The Khan Academy.


Khan academy is outstanding. There is a wealth of other stuff on the net. My oldest daughter had gotten straight As in math up through HS and a 5 on her AP BC. Her first math class in college was linear algebra (or maybe it was differential equations ... I don't remember exactly) and she was making Cs and Ds. This was really odd, because linear algebra is USUALLY a cake-walk after you've already had calculus.

Anyway, she stopped going to class and started instead to watch MITs OpenCourseware videos, http://ocw.mit.edu/index.htm . Here grades immediately jumped back up to As. By end of semester it averaged out to a B (or maybe a B+). Anyway, there's some *really* good available now on a variety of topics if we have the patience to wade through it - from Yale, Berkeley, MIT, many others.

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Would I be right in thinking that:

4m^2 = a 2x2 grid, with each cell being a 1mx1m.

but,

(4m)^2 = a 4x4 grid, with each cell being a 1mx1m.

Just a thought from a non-mathematician smile


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