mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Miscellaneous Math

Reply
 
Thread Tools
Old 2012-11-27, 18:14   #1
Flatlander
I quite division it
 
Flatlander's Avatar
 
"Chris"
Feb 2005
England

31·67 Posts
Default 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
Click image for larger version

Name:	image.jpg
Views:	232
Size:	61.3 KB
ID:	8915  
Flatlander is offline   Reply With Quote
Old 2012-11-27, 18:55   #2
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

32·1,117 Posts
Default

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.
Batalov is offline   Reply With Quote
Old 2012-11-27, 20:11   #3
NBtarheel_33
 
NBtarheel_33's Avatar
 
"Nathan"
Jul 2008
Maryland, USA

100010110112 Posts
Default

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.
NBtarheel_33 is offline   Reply With Quote
Old 2012-11-27, 20:43   #4
frmky
 
frmky's Avatar
 
Jul 2003
So Cal

22×11×59 Posts
Default

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.
frmky is offline   Reply With Quote
Old 2012-11-28, 02:22   #5
LaurV
Romulan Interpreter
 
LaurV's Avatar
 
"name field"
Jun 2011
Thailand

1027410 Posts
Default

Quote:
Originally Posted by NBtarheel_33 View Post
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 View Post
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...

Last fiddled with by LaurV on 2012-11-28 at 02:23
LaurV is online now   Reply With Quote
Old 2012-11-28, 16:51   #6
Flatlander
I quite division it
 
Flatlander's Avatar
 
"Chris"
Feb 2005
England

31·67 Posts
Default

I pronounce these as 'sixty-four pling', like a rather depressed microwave. Don't know where I picked that up.
Flatlander is offline   Reply With Quote
Old 2012-11-28, 17:19   #7
bsquared
 
bsquared's Avatar
 
"Ben"
Feb 2007

7·13·41 Posts
Default

Many people would maybe use a 'click' (although probably not English speakers), for example, the !Kung.
bsquared is offline   Reply With Quote
Old 2012-11-28, 20:55   #8
NBtarheel_33
 
NBtarheel_33's Avatar
 
"Nathan"
Jul 2008
Maryland, USA

111510 Posts
Default

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!?
NBtarheel_33 is offline   Reply With Quote
Old 2012-11-28, 21:26   #9
Dubslow
Basketry That Evening!
 
Dubslow's Avatar
 
"Bunslow the Bold"
Jun 2011
40<A<43 -89<O<-88

3×29×83 Posts
Default

Quote:
Originally Posted by NBtarheel_33 View Post
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
Dubslow is offline   Reply With Quote
Old 2012-11-28, 21:36   #10
bsquared
 
bsquared's Avatar
 
"Ben"
Feb 2007

7×13×41 Posts
Default

Generalizing to any m! with n least terms missing:

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

bsquared is offline   Reply With Quote
Old 2012-11-28, 22:18   #11
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

32×1,117 Posts
Default

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.
Batalov is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Playing with decimal representation Nick Puzzles 9 2013-02-13 17:17
Musing on TF limits davieddy Lounge 10 2012-12-04 18:43
Searching for m. primes is like playing lottery joblack Lounge 20 2009-01-05 15:18
Playing with different radix LoveCraft Programming 7 2005-11-14 07:59
playing with numbers michael Puzzles 14 2004-01-17 00:15

All times are UTC. The time now is 08:58.


Mon Jan 30 08:58:36 UTC 2023 up 165 days, 6:27, 0 users, load averages: 1.42, 1.04, 0.94

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2023, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.

≠ ± ∓ ÷ × · − √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °
∠ ∟ ° ≅ ~ ‖ ⟂ ⫛
≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘ ∏ ∐ ∑ ∧ ∨ ∩ ∪ ⨀ ⊕ ⊗ 𝖕 𝖖 𝖗 ⊲ ⊳
∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟
¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣ … ⋯ ⋮ ⋰ ⋱
∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ
𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎𝜍 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔