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The Magic Cafe Forum Index » » Not very magical, still... » » A math question for Landmark and other mathematicians (0 Likes) Printer Friendly Version

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Jack Straw
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I'm directing this towards Landmark simply because I know that he teaches or taught mathematics at good schools in NYC, and was also a private math tutor.

But anyone who really knows math can chime in here.

There is no room in math for speculation and guesses and I believes, so please do not answer with those kind of statements.

I'm having a little disagreement in another actual magic thread concerning the size of a Jumbo Deck of cards.

It has been claimed that a Jumbo Deck is "Four times the size of a regular deck".

I insist that "Four times the size" of a normal, 3 1/2" x 2 1/2" deck is 14" x 10", but all others claim that 7" x 5" is four times the size.

7" x 5" is 4 times the AREA, but NOT 4 times the SIZE.

Size and area are two entirely different things.

14" x 10" is four times the SIZE, correct?

Thanks, Jack
Jack Straw from Wichita, cut his buddy down
And dug for him a shallow grave, and laid his body down
Half a mile from Tucson, by the morning light
One man gone and another to go, my old buddy you're moving much too slow
We can share the women, we can share the wine
Magnus Eisengrim
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"Size" is an imprecise term. As you note in the argument, if you are speaking of individual cards, you could 4 times the area or 4 times the linear dimensions (I suppose there are other weird transformaitonal possibilities, too.)

When dealing with the entire deck, you could also talk about 4 times the volume.

In the end, the problem is that "Four times the size" is not a clearly-defined metric.
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity.--Yeats
Jack Straw
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I disagree, Magnus.

Size is a very specific term.

4 x 3 1/2= 14, and 4 x 2 1/2= 10.

You must multiply both dimensions by 4 to come up with a proper answer.

Therefore, four times the size of a normal deck is a deck that measures 14" x 10".

Four times the area, which is also a very specific term, is 7" x 5".
Jack Straw from Wichita, cut his buddy down
And dug for him a shallow grave, and laid his body down
Half a mile from Tucson, by the morning light
One man gone and another to go, my old buddy you're moving much too slow
We can share the women, we can share the wine
Jack Straw
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If I put a playing card into a copying machine that enlarges 4 times, I end up with a 14" x 10" card.

It is very precise.

No guesswork.
Jack Straw from Wichita, cut his buddy down
And dug for him a shallow grave, and laid his body down
Half a mile from Tucson, by the morning light
One man gone and another to go, my old buddy you're moving much too slow
We can share the women, we can share the wine
balducci
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Quote:
On 2014-02-06 10:26, Magnus Eisengrim wrote:

"Size" is an imprecise term. As you note in the argument, if you are speaking of individual cards, you could 4 times the area or 4 times the linear dimensions (I suppose there are other weird transformaitonal possibilities, too.)

When dealing with the entire deck, you could also talk about 4 times the volume.

In the end, the problem is that "Four times the size" is not a clearly-defined metric.

+1 Agreed.

"Size" is an ambiguous term.

Size may be in reference to a volume, size may be in reference to an area, size may be in reference to a height, or size may be in reference to some other feature.

Size may even be in reference (count) the number of spades on a card. So a 7 of spades has size 7, regardless of its length or width. An 8 of hearts has size 0.
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Jack Straw
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If I have a square that is 2" x2", and I enlarge it to twice the size, I end up with an object that is 4" x 4", not 4" x 2".

4" x 2" is not a square anymore, but it has twice the area of the original object- not twice the size, though!
Jack Straw from Wichita, cut his buddy down
And dug for him a shallow grave, and laid his body down
Half a mile from Tucson, by the morning light
One man gone and another to go, my old buddy you're moving much too slow
We can share the women, we can share the wine
S2000magician
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While I agree with Magnus - actuarially, a good policy - I would say that to most people the "size" of a playing card would be the area of its face. While I don't claim to be an expert (or even an authority) on human perception, I believe that most people would measure the size of a playing card as the area of its face. Therefore, jumbo cards, with dimensions twice those of normal playing cards (side note: bridge size, or poker size?), would be considered four times as large.

I've never taught mathematics at good schools in NYC, but I did teach mathematics at California State University, Fullerton for twenty years, for whatever that's worth.
balducci
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Jack, the good news is that both you and your 'friends' are correct according to your own interpretations of size.

However, I think your friend's interpretation of size is probably the one that most people would use in this particular context.
Make America Great Again! - Trump in 2020 ... "We're a capitalistic society. I go into business, I don't make it, I go bankrupt. They're not going to bail me out. I've been on welfare and food stamps. Did anyone help me? No." - Craig T. Nelson, actor.
Jack Straw
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Just because most people would use that interpretation does not make it correct.
Jack Straw from Wichita, cut his buddy down
And dug for him a shallow grave, and laid his body down
Half a mile from Tucson, by the morning light
One man gone and another to go, my old buddy you're moving much too slow
We can share the women, we can share the wine
S2000magician
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Quote:
On 2014-02-06 11:01, Jack Straw wrote:
Just because most people would use that interpretation does not make it correct.

Nor does it make it incorrect.

Note that I began by agreeing with Magnus. That's key.
balducci
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Quote:
On 2014-02-06 10:49, S2000magician wrote:
While I agree with Magnus - actuarially, a good policy - I would say that to most people the "size" of a playing card would be the area of its face. While I don't claim to be an expert (or even an authority) on human perception, I believe that most people would measure the size of a playing card as the area of its face. Therefore, jumbo cards, with dimensions twice those of normal playing cards (side note: bridge size, or poker size?), would be considered four times as large.

I've never taught mathematics at good schools in NYC, but I did teach mathematics at California State University, Fullerton for twenty years, for whatever that's worth.

So it appears that three people who have taught mathematics, at least some of whom also have advanced degrees in the subject, are basically onside.

Jack is still arguing with / correcting them.

So much for the value of "expertise". Smile

Jack, why did you even ask what the mathematicians think? Smile Smile
Make America Great Again! - Trump in 2020 ... "We're a capitalistic society. I go into business, I don't make it, I go bankrupt. They're not going to bail me out. I've been on welfare and food stamps. Did anyone help me? No." - Craig T. Nelson, actor.
Jack Straw
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I do not know the qualifications of the answerers, except for s2000.

No offense.

I'm at work and cannot give comprehensive statements here, but I certainly do have more to say about it.
Jack Straw from Wichita, cut his buddy down
And dug for him a shallow grave, and laid his body down
Half a mile from Tucson, by the morning light
One man gone and another to go, my old buddy you're moving much too slow
We can share the women, we can share the wine
Jack Straw
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But I'll ask again-

If I blow up a 2" square to twice the size, I end up with a 4" x 2" rectangle?
Jack Straw from Wichita, cut his buddy down
And dug for him a shallow grave, and laid his body down
Half a mile from Tucson, by the morning light
One man gone and another to go, my old buddy you're moving much too slow
We can share the women, we can share the wine
stoneunhinged
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The point at issue is that size is the point at which there is a correspondence between assessments of material reality according to the senses comparative to the correspondence between perceptions of those assessments. Should we believe that our assessments are not inapposite to our perceptions, then there exists a robasculation of signification of the "what is" in contradistinction to the "what I see", and rightly so.

So I agree with Jack Straw 200%, irregardless of the sophistic over-exaggerations of Café mathematicians.
Marlin1894
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Yep, the old robasculation of signification gets you every time.
Jack Straw
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Love your answer, stoneunhinged!

I needed to laugh today!
Jack Straw from Wichita, cut his buddy down
And dug for him a shallow grave, and laid his body down
Half a mile from Tucson, by the morning light
One man gone and another to go, my old buddy you're moving much too slow
We can share the women, we can share the wine
S2000magician
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I always agree with Jeff (stoney) without reservation. It's simpler that way.
Magnus Eisengrim
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Quote:
On 2014-02-06 11:12, Jack Straw wrote:
But I'll ask again-

If I blow up a 2" square to twice the size, I end up with a 4" x 2" rectangle?


I have two suggestions:

1. Withdraw the mathematical question and ask professional printers and graphic artists, as they have trade-specific definitions that you will agree with.
2. Don't ask questions if you aren't prepared to hear the answers.
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity.--Yeats
S2000magician
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Quote:
On 2014-02-06 11:12, Jack Straw wrote:
But I'll ask again-

If I blow up a 2" square to twice the size, I end up with a 4" x 2" rectangle?

I'd think that you'd end up with another square, 2.82842712474619 . . ." × 2.82842712474619 . . .".
Jack Straw
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I am a professional printer and graphic designer, Magnus.

I'm working in "Indesign" on a job as we speak.

And that's why I know what it means to enlarge something 4 times.
Jack Straw from Wichita, cut his buddy down
And dug for him a shallow grave, and laid his body down
Half a mile from Tucson, by the morning light
One man gone and another to go, my old buddy you're moving much too slow
We can share the women, we can share the wine
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