An independent forum site for members of the Serif software community
You are not logged in. Please login or register.
Automated signup has been disabled for these forums. If you wish to register, please send an email to admin[at]punster[dot]me stating your preferred username.
Embedded images: Click on the 
Add image to post link below the message box. Your photo will be uploaded to the postimage website and then shared here via a thumbnail link. Click on the thumbnail for a larger view.
Private messages: There is no pop-up alert for new PMs on these forums, so you need to look out for the PM link (near the top right-hand corner of any forum page) becoming bold.
Alfred's Serif Users' Forums → Mathematics & Science → Reinventing the magic log wheel: How was this missed for 400 years?
A Mathologer video.
A novel way of demonstrating the circular slide rule - stretch a rubber band round the disk.
Today is about reinventing a really cool mathematical wheel and its many different slide rule incarnations, just using a rubber band.
https://www.youtube.com/watch?v=ZIQQvxSXLhI
Interesting and informative (as Mathologer so often is). Thanks for the link, Jack!
I have been trying to rationalise why the scale is natural log...
My mind is sadly too feeble at this moment to originate a proof, but I can post a comment from the Mathologer piece:
Proof of the length of the wheel being ln(10) :
When the number x reaches the wheel, the rubber band has stretched by a factor 1/x (we consider that the rubber band is numbered from 0 to 1 like in the video). If you now wind the band just a bit more so that you reach x+dx (with dx infinitesimal), then the length added on the wheel is dl=a(x)dx. So the total length of the wheel is the integral of dl for x=0.1 to 1 that is int(dx/x, x=0.1..1), which is equal to ln(10).
I was getting there myself, but couldn't put it together. Obviously my cogs don't always mesh.
If the rubber band has stretched along its length, why are the numbers not spaced evenly around the wheel?
What am I missing please?
William
What am I missing please?
The parts of the rubber band no longer stretch after they contact with the wheel. Imagine the wheel is coated with superglue.
Thank you.
William
Alfred's Serif Users' Forums → Mathematics & Science → Reinventing the magic log wheel: How was this missed for 400 years?
Powered by PunBB, supported by Informer Technologies, Inc.