Go Back   Freethought Forum > The Marketplace > Study Hall

Reply
 
Thread Tools Display Modes
  #26  
Old 10-14-2020, 05:51 PM
Pan Narrans's Avatar
Pan Narrans Pan Narrans is offline
Give my creation life!
 
Join Date: Oct 2007
Location: Utrecht, the Netherlands
Gender: Male
Posts: MXDCCXLIX
Default Re: Geometry puzzle

(60/37)2
__________________
:beneluxmafia:
Reply With Quote
Thanks, from:
ceptimus (10-14-2020)
  #27  
Old 10-14-2020, 06:12 PM
ceptimus's Avatar
ceptimus ceptimus is offline
puzzler
 
Join Date: Aug 2004
Location: UK
Posts: XVMCCCXCVII
Images: 28
Default Re: Geometry puzzle

Again, Pan wins the prize for the first correct answer!

:medal:

This one was easier (I think) than the last one, but I found it oddly satisfying. The 60 in the answer, one might expect - it is, after all, 3 x 4 x 5 - but I would never have guessed the 37.
__________________
Reply With Quote
Thanks, from:
Pan Narrans (10-14-2020)
  #28  
Old 10-15-2020, 08:30 AM
Pan Narrans's Avatar
Pan Narrans Pan Narrans is offline
Give my creation life!
 
Join Date: Oct 2007
Location: Utrecht, the Netherlands
Gender: Male
Posts: MXDCCXLIX
Default Re: Geometry puzzle

As for how I came to the answer:

Attached Images
File Type: gif 345square.gif (9.9 KB, 20 views)
__________________
:beneluxmafia:
Reply With Quote
Thanks, from:
ceptimus (10-15-2020), Crumb (10-15-2020), JoeP (10-15-2020), SR71 (10-16-2020)
  #29  
Old 10-15-2020, 08:39 AM
Pan Narrans's Avatar
Pan Narrans Pan Narrans is offline
Give my creation life!
 
Join Date: Oct 2007
Location: Utrecht, the Netherlands
Gender: Male
Posts: MXDCCXLIX
Default Re: Geometry puzzle

Quote:
Originally Posted by ceptimus View Post
Again, Pan wins the prize for the first correct answer!

:medal:

This one was easier (I think) than the last one, but I found it oddly satisfying. The 60 in the answer, one might expect - it is, after all, 3 x 4 x 5 - but I would never have guessed the 37.
Dimensional analysis can work here.

If you figure 3 * 4 * 5 has to be in there, this has units of [length]3. If you want to go to a single [length], you have to divide by [length]2.

One side of the square coincides with the hypothenuse of the triangle, so the 5 warrants special treatment here. To get a [length]2, one might try 3*5 + 4*5 (=35, not quite right) or 3*4 + 5*5 (=37, the right answer).

Of course, this is hand-waving after the fact, but the number 37 does not just pop out of nowhere.
__________________
:beneluxmafia:
Reply With Quote
Thanks, from:
ceptimus (10-15-2020), SR71 (10-16-2020)
  #30  
Old 10-15-2020, 01:24 PM
ceptimus's Avatar
ceptimus ceptimus is offline
puzzler
 
Join Date: Aug 2004
Location: UK
Posts: XVMCCCXCVII
Images: 28
Default Re: Geometry puzzle

Yes. So my conjecture is that this works for any square drawn in a right triangle.
__________________
Reply With Quote
Thanks, from:
Pan Narrans (10-15-2020)
  #31  
Old 10-15-2020, 01:38 PM
ceptimus's Avatar
ceptimus ceptimus is offline
puzzler
 
Join Date: Aug 2004
Location: UK
Posts: XVMCCCXCVII
Images: 28
Default Re: Geometry puzzle

Quote:
Originally Posted by Pan Narrans View Post
As for how I came to the answer:

__________________
Reply With Quote
Thanks, from:
Crumb (10-15-2020), Pan Narrans (10-15-2020), SR71 (10-16-2020)
  #32  
Old 10-15-2020, 05:42 PM
ceptimus's Avatar
ceptimus ceptimus is offline
puzzler
 
Join Date: Aug 2004
Location: UK
Posts: XVMCCCXCVII
Images: 28
Default Re: Geometry puzzle

As a quick check, here's the 5:12:13 Pythagorean triangle drawn in Fusion 360. You can see that the CAD program puts the dimension for the side of the square in parentheses: in CAD terms this is a "driven dimension" - you can't actually enter a value because the size is already fixed by the dimensions and constraints already specified.



You can see that Fusion 360 shows the length as 3.406, which, to three decimal places, is indeed 780/229
Attached Images
File Type: gif 5-12-13square.gif (8.1 KB, 13 views)
__________________

Last edited by ceptimus; 10-15-2020 at 06:19 PM.
Reply With Quote
Thanks, from:
Crumb (10-15-2020), Pan Narrans (10-15-2020), SR71 (10-16-2020)
Reply

  Freethought Forum > The Marketplace > Study Hall


Currently Active Users Viewing This Thread: 1 (0 members and 1 guests)
 
Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump

 

All times are GMT +1. The time now is 10:50 PM.


Powered by vBulletin® Version 3.8.2
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.
Page generated in 0.18465 seconds with 15 queries