Playing with WolframAlpha and musing.

Flatlander · 2012-11-27, 18:14

As someone who really struggles with maths I am interested in what a person with a 'good mathematical understanding'* sees when they look at something like this.

Do they look at this and just understand or is this not obvious to such a person?

*Define as appropriate.

Batalov · 2012-11-27, 18:55

WolframAlpha is really good for one-offs: say you don't want to derive (and don't remember by heart) Sum(0<=i<=n)i^3, then it will tell you!
However, with a little more obscure requests, it gives you some fluff, i.e. it tries to be helpful and applies every possible diversion, and every once in a while is been almost sarcastic (it would seem ;-) to the point of being absurd.

NBtarheel_33 · 2012-11-27, 20:11

I have an advanced degree in math(s), if that counts, and I can tell you that the "simplification" provided by Alpha is something that no one (outside of a student trying to be a smart aleck) would ever make serious use of. It would be akin to asking for a glass of "aqueous dihydrogen monoxide" rather than "water". I suspect that it is an example of the computer's AI scheme running amok.

On the other hand, at least it didn't reply to 64!/32! by loudly chanting "SIXTY-FOUR! over THIRTY-TWO!". There was a guy in a *college* class of mine that actually saw 3! and pronounced it "THREE!" and wondered why they wanted us to shout the numbers.

frmky · 2012-11-27, 20:43

Breaking it down, I first notice that $-1+\cos(128\pi)$ and $-1+\cos(64\pi)$ are both 0, so those terms drop out. Then, $2^{-64}/2^{-32} = 1/2^{32}$ . Next, $\sin(64\pi)$ and $\sin(32\pi)$ are both 0, so $\pi^0$ is simply 1. Thus we conclude that this was constructed by a joker trying to be cute.

We are then left with $\frac{64!}{32!}=\frac{128!!}{64!! \times 2^{32}$ . This becomes clear one you write out a few terms of the expansion.

LaurV · 2012-11-28, 02:22

Quote:

Originally Posted by NBtarheel_33

There was a guy in a *college* class of mine that actually saw 3! and pronounced it "THREE!" and wondered why they wanted us to shout the numbers.

(this is cool, I have to remember it!

)

Quote:

Originally Posted by frmky

We are then left with $\frac{64!}{32!}=\frac{128!!}{64!! \times 2^{32}$ . This becomes clear one you write out a few terms of the expansion.

According with the former, the last should be ONE HUNDRED TWENTY EIGHT!! etc...

Flatlander · 2012-11-28, 16:51

I pronounce these as 'sixty-four pling', like a rather depressed microwave. Don't know where I picked that up.

bsquared · 2012-11-28, 17:19

Many people would maybe use a 'click' (although probably not English speakers), for example, the !Kung.

NBtarheel_33 · 2012-11-28, 20:55

So, is there a symbol for "factorial missing the least n terms"? For instance, is there a notation for 64!/32! other than 64!/32!?

Dubslow · 2012-11-28, 21:26

Quote:

Originally Posted by NBtarheel_33

So, is there a symbol for "factorial missing the least n terms"? For instance, is there a notation for 64!/32! other than 64!/32!?

$\prod_{i=33}^{64}i$

bsquared · 2012-11-28, 21:36

Generalizing to any m! with n least terms missing:

$\prod_{i=m-n+1}^{m}i$

Batalov · 2012-11-28, 22:18

Relevant to PE 403, try this:
Sum(over odd d from d₁ to d₂) (2 + (d³+5d)/3)
and the same for even d values.

2012-11-27, 18:14	#1
Flatlander I quite division it "Chris" Feb 2005 England 31·67 Posts	Playing with WolframAlpha and musing. As someone who really struggles with maths I am interested in what a person with a 'good mathematical understanding'* sees when they look at something like this. Do they look at this and just understand or is this not obvious to such a person? *Define as appropriate. Attached Thumbnails

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2012-11-27, 18:55	#2
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,497 Posts	WolframAlpha is really good for one-offs: say you don't want to derive (and don't remember by heart) Sum(0<=i<=n)i^3, then it will tell you! However, with a little more obscure requests, it gives you some fluff, i.e. it tries to be helpful and applies every possible diversion, and every once in a while is been almost sarcastic (it would seem ;-) to the point of being absurd.

2012-11-27, 20:11	#3
NBtarheel_33 "Nathan" Jul 2008 Maryland, USA 10001011011₂ Posts	I have an advanced degree in math(s), if that counts, and I can tell you that the "simplification" provided by Alpha is something that no one (outside of a student trying to be a smart aleck) would ever make serious use of. It would be akin to asking for a glass of "aqueous dihydrogen monoxide" rather than "water". I suspect that it is an example of the computer's AI scheme running amok. On the other hand, at least it didn't reply to 64!/32! by loudly chanting "SIXTY-FOUR! over THIRTY-TWO!". There was a guy in a college class of mine that actually saw 3! and pronounced it "THREE!" and wondered why they wanted us to shout the numbers.

2012-11-27, 20:43	#4
frmky Jul 2003 So Cal 2⁴·7·19 Posts	Breaking it down, I first notice that $-1+\cos(128\pi)$ and $-1+\cos(64\pi)$ are both 0, so those terms drop out. Then, $2^{-64}/2^{-32} = 1/2^{32}$ . Next, $\sin(64\pi)$ and $\sin(32\pi)$ are both 0, so $\pi^0$ is simply 1. Thus we conclude that this was constructed by a joker trying to be cute. We are then left with $\frac{64!}{32!}=\frac{128!!}{64!! \times 2^{32}$ . This becomes clear one you write out a few terms of the expansion.

2012-11-28, 16:51	#6
Flatlander I quite division it "Chris" Feb 2005 England 31·67 Posts	I pronounce these as 'sixty-four pling', like a rather depressed microwave. Don't know where I picked that up.

2012-11-28, 17:19	#7
bsquared "Ben" Feb 2007 110111000010₂ Posts	Many people would maybe use a 'click' (although probably not English speakers), for example, the !Kung.

2012-11-28, 20:55	#8
NBtarheel_33 "Nathan" Jul 2008 Maryland, USA 10001011011₂ Posts	So, is there a symbol for "factorial missing the least n terms"? For instance, is there a notation for 64!/32! other than 64!/32!?

2012-11-28, 21:36	#10
bsquared "Ben" Feb 2007 6702₈ Posts	Generalizing to any m! with n least terms missing: $\prod_{i=m-n+1}^{m}i$

2012-11-28, 22:18	#11
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,497 Posts	Relevant to PE 403, try this: Sum(over odd d from d₁ to d₂) (2 + (d³+5d)/3) and the same for even d values.