The Imaginary Pricing Department Store
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5 members have voted
Many years later, an entire industry was born who studied the psychological dimension of pricing. They discovered that people would flock to items marked $3.99 or $3.95 over other identical items priced at, say $4.04.
Fast forward to the future, when the human race has further evolved and people demand not only a bargain but a math challenge as well. This department store "of the future" uses combinations of imaginary numbers for pricing and requires you to ask yourself:
Would I pay i^i (i, the square root of -1, raised to the i'th power) dollars for an item worth (in conventional terms) $.50?
[PLEASE use spoiler tags to allow people, if any, who may not be familiar with this a chance to try it.]
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"The only thing that's new in the world is the history you don't know." --Harry S. Truman
Quote: dblanch256The first reliably dated department store to be established, was Harding, Howell & Co, which opened in 1796 on Pall Mall, London. Placing price tags on items was considered revolutionary, but good for business because it cut down on the time required to negotiate a sale.
Many years later, an entire industry was born who studied the psychological dimension of pricing. They discovered that people would flock to items marked $3.99 or $3.95 over other identical items priced at, say $4.04.
Fast forward to the future, when the human race has further evolved and people demand not only a bargain but a math challenge as well. This department store "of the future" uses combinations of imaginary numbers for pricing and requires you to ask yourself:
Would I pay i^i (i, the square root of -1, raised to the i'th power) dollars for an item worth (in conventional terms) $.50?
[PLEASE use spoiler tags to allow people, if any, who may not be familiar with this a chance to try it.]
=======================================================================================
"The only thing that's new in the world is the history you don't know." --Harry S. Truman
Welcome back, Fred.
ii = (eln i)i = ei ln i
ei PI/2 = cos PI/2 + i sin PI/2 = i, so ln i = i PI/2
ei ln i = ei * (i PI/2) = e-PI/2 = 0.20788
https://wizardofvegas.com/forum/questions-and-answers/math/15393-what-does-e-pi-i-equal/
and the one it refers to. We have had that discussion already.
But then when we were married, Babs saved me so much shopping that I had to declare bankruptcy.
Quote: beachbumbabsQuote: dblanch256The first reliably dated department store to be established, was Harding, Howell & Co, which opened in 1796 on Pall Mall, London. Placing price tags on items was considered revolutionary, but good for business because it cut down on the time required to negotiate a sale.
Many years later, an entire industry was born who studied the psychological dimension of pricing. They discovered that people would flock to items marked $3.99 or $3.95 over other identical items priced at, say $4.04.
Fast forward to the future, when the human race has further evolved and people demand not only a bargain but a math challenge as well. This department store "of the future" uses combinations of imaginary numbers for pricing and requires you to ask yourself:
Would I pay i^i (i, the square root of -1, raised to the i'th power) dollars for an item worth (in conventional terms) $.50?
[PLEASE use spoiler tags to allow people, if any, who may not be familiar with this a chance to try it.]
=======================================================================================
"The only thing that's new in the world is the history you don't know." --Harry S. Truman
Welcome back, Fred.
(1) Quite correct!
(2) Sorry, but I'm getting a different answer. Would you consider "showing your work"? Maybe we can get to the bottom of this. Regardless, thanks for heeding the Spoiler button request!yes, I would buy that; i^i = 0.20787957635, or a bargain at 59% off!
Quote: dblanch256Quote: beachbumbabsQuote: dblanch256The first reliably dated department store to be established, was Harding, Howell & Co, which opened in 1796 on Pall Mall, London. Placing price tags on items was considered revolutionary, but good for business because it cut down on the time required to negotiate a sale.
Many years later, an entire industry was born who studied the psychological dimension of pricing. They discovered that people would flock to items marked $3.99 or $3.95 over other identical items priced at, say $4.04.
Fast forward to the future, when the human race has further evolved and people demand not only a bargain but a math challenge as well. This department store "of the future" uses combinations of imaginary numbers for pricing and requires you to ask yourself:
Would I pay i^i (i, the square root of -1, raised to the i'th power) dollars for an item worth (in conventional terms) $.50?
[PLEASE use spoiler tags to allow people, if any, who may not be familiar with this a chance to try it.]
=======================================================================================
"The only thing that's new in the world is the history you don't know." --Harry S. Truman
Welcome back, Fred.
(1) Who is Fred?
(2) Quite Correct.yes, I would buy that; i^i = 0.20787957635, or a bargain at 59% off!
Quote: dblanch256Quote: dblanch256Quote: beachbumbabsQuote: dblanch256The first reliably dated department store to be established, was Harding, Howell & Co, which opened in 1796 on Pall Mall, London. Placing price tags on items was considered revolutionary, but good for business because it cut down on the time required to negotiate a sale.
Many years later, an entire industry was born who studied the psychological dimension of pricing. They discovered that people would flock to items marked $3.99 or $3.95 over other identical items priced at, say $4.04.
Fast forward to the future, when the human race has further evolved and people demand not only a bargain but a math challenge as well. This department store "of the future" uses combinations of imaginary numbers for pricing and requires you to ask yourself:
Would I pay i^i (i, the square root of -1, raised to the i'th power) dollars for an item worth (in conventional terms) $.50?
[PLEASE use spoiler tags to allow people, if any, who may not be familiar with this a chance to try it.]
=======================================================================================
"The only thing that's new in the world is the history you don't know." --Harry S. Truman
Welcome back, Fred.
(1) Who is Fred?
(2) Quite Correctyes, I would buy that; i^i = 0.20787957635, or a bargain at 59% off!
Quote: kubikulannYou''l want to read that thread
https://wizardofvegas.com/forum/questions-and-answers/math/15393-what-does-e-pi-i-equal/
and the one it refers to. We have had that discussion already.
I went to that thread, which has over 100 posts in it. I saw many variations of Eulers equation, but not this specific problem.
However, I take you at your word that it exists in there somewhere. Thanks for the link.
Quote: ThatDonGuy
ii = (eln i)i = ei ln i
ei PI/2 = cos PI/2 + i sin PI/2 = i, so ln i = i PI/2
ei ln i = ei * (i PI/2) = e-PI/2 = 0.20788
Shorter version might be that since e^(i theta) is the unit vector in complex plan with angle theta,
i = e^(i theta) is true when theta = pi/2. Resulting in, well, what you got.
Using a^b = exp(b * ln a), so
i^i = exp(i * ln i) = exp (i * i*pi/2) = 0.208...
But this does not imply you should buy it if it's worth .5 - this depends if you either want the item or could sell it otherwise.
Quote: MangoJ
Using a^b = exp(b * ln a), so
i^i = exp(i * ln i) = exp (i * i*pi/2) = 0.208...
But this does not imply you should buy it if it's worth .5 - this depends if you either want the item or could sell it otherwise.
Good point, and well done!
If it takes all this to figure out a price ain't nobody gonna be buying no products in this store of imaginary numbers.
People might start going to such a store ... you know, make-up, perfume, etc. then go shopping at the store of imaginary numbers and soon to be rich tech heads but it won't have anything to do with prices for the transactions that take place there.
