0 members (),
619
guests, and
2
robots. |
Key:
Admin,
Global Mod,
Mod
|
|
|
Joined: Aug 2010
Posts: 3,570
Megastar
|
Megastar
Joined: Aug 2010
Posts: 3,570 |
Good link, TFF. I could with that sort of explatation for the more complex stuff.
There never was nothing.
|
|
|
|
Joined: Jun 2005
Posts: 1,940
Megastar
|
Megastar
Joined: Jun 2005
Posts: 1,940 |
Bill, is there anything specific that you're looking for?
|
|
|
|
Joined: Aug 2010
Posts: 3,570
Megastar
|
Megastar
Joined: Aug 2010
Posts: 3,570 |
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.
There never was nothing.
|
|
|
|
Joined: Mar 2006
Posts: 4,136
Megastar
|
OP
Megastar
Joined: Mar 2006
Posts: 4,136 |
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.
3/4 inch of dust build up on the moon in 4.527 billion years,LOL and QM is fantasy science.
|
|
|
|
Joined: Jun 2005
Posts: 1,940
Megastar
|
Megastar
Joined: Jun 2005
Posts: 1,940 |
|
|
|
|
Joined: Aug 2010
Posts: 3,570
Megastar
|
Megastar
Joined: Aug 2010
Posts: 3,570 |
Thanks, TFF.
Duty calls, but I'll have a look at those links a bit later.
There never was nothing.
|
|
|
|
Joined: Jun 2005
Posts: 1,940
Megastar
|
Megastar
Joined: Jun 2005
Posts: 1,940 |
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.
|
|
|
|
Joined: Mar 2006
Posts: 4,136
Megastar
|
OP
Megastar
Joined: Mar 2006
Posts: 4,136 |
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)
3/4 inch of dust build up on the moon in 4.527 billion years,LOL and QM is fantasy science.
|
|
|
|
Joined: Mar 2006
Posts: 4,136
Megastar
|
OP
Megastar
Joined: Mar 2006
Posts: 4,136 |
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 squared4 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
3/4 inch of dust build up on the moon in 4.527 billion years,LOL and QM is fantasy science.
|
|
|
|
Joined: Mar 2006
Posts: 4,136
Megastar
|
OP
Megastar
Joined: Mar 2006
Posts: 4,136 |
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 4 ft * 4 ft = 16 ft
3/4 inch of dust build up on the moon in 4.527 billion years,LOL and QM is fantasy science.
|
|
|
|
Joined: Jun 2005
Posts: 1,940
Megastar
|
Megastar
Joined: Jun 2005
Posts: 1,940 |
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.)
|
|
|
|
Joined: Mar 2006
Posts: 4,136
Megastar
|
OP
Megastar
Joined: Mar 2006
Posts: 4,136 |
write that out use the smiley for square ie... 4 ft or 4 ft both the above have the same value.
3/4 inch of dust build up on the moon in 4.527 billion years,LOL and QM is fantasy science.
|
|
|
|
Joined: Jun 2005
Posts: 1,940
Megastar
|
Megastar
Joined: Jun 2005
Posts: 1,940 |
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.
|
|
|
|
Joined: Mar 2006
Posts: 4,136
Megastar
|
OP
Megastar
Joined: Mar 2006
Posts: 4,136 |
3/4 inch of dust build up on the moon in 4.527 billion years,LOL and QM is fantasy science.
|
|
|
|
Joined: Dec 2010
Posts: 1,858
Megastar
|
Megastar
Joined: Dec 2010
Posts: 1,858 |
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.
|
|
|
|
Joined: Jun 2005
Posts: 1,940
Megastar
|
Megastar
Joined: Jun 2005
Posts: 1,940 |
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.
Last edited by TheFallibleFiend; 10/07/11 08:19 PM.
|
|
|
|
Joined: Mar 2006
Posts: 4,136
Megastar
|
OP
Megastar
Joined: Mar 2006
Posts: 4,136 |
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.
3/4 inch of dust build up on the moon in 4.527 billion years,LOL and QM is fantasy science.
|
|
|
|
Joined: Jun 2005
Posts: 1,940
Megastar
|
Megastar
Joined: Jun 2005
Posts: 1,940 |
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.
|
|
|
|
Joined: Jun 2005
Posts: 1,940
Megastar
|
Megastar
Joined: Jun 2005
Posts: 1,940 |
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.
|
|
|
|
Joined: Aug 2010
Posts: 3,570
Megastar
|
Megastar
Joined: Aug 2010
Posts: 3,570 |
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
There never was nothing.
|
|
|
|
|