trivia - trisecting an angle & gradians

[steamingbill]

See this video at 24:00 regarding making a cog with a given number of teeth ...

https://www.youtube.com/watch?v=nZXjUqLMgxM

Paul,

Many thanks for the fascinating links - I didnt know about that thing and clearly they were able to divide up circles and play with angles and geometry with a high levele of understanding and metalwork skills.

The manual cog cutting technique reminded me of something I'd read recently about dividing wheels where there could be (maybe ?) a way of estimating the dividing holes on a first attempt at a dividing wheel and then sticking it on the dividing head and then using the dividing head somehow to make the second one more accurate - I dont know enough about how that works but will find the book and post it here in case anyone is interested. Maybe I am raving - must find the book I was reading a few days ago and check it.


Found a link - I dont understand this idea yet but somebody may be interested. Probably discussed in many places.

http://www.homews.co.uk/page427.html
Bill

[pmcgee]

This is how I read it ...

Anyone can gauge a full rotation perfectly accurately, assuming the fit of the shaft and etc parts, with just a single mark.
If everything else is up to scratch, then 1 rotation will bring you to the same place every time,
and with eg a 40x reduction gear, each full rotation should give you precisely 9^o on your workpiece.

So eg to mark 40^o on your workpiece, you need to move 36^o by full rotations plus 4^o by a part rotation (of the divider).

The part rotation will be 160^o on the divider, which we assume is accurate to +- x degrees.

So the resulting movement of the workpiece will be 4^o +-(x/40) degrees ... total movement 40^o +-(x/40) and you've increased your accuracy 40x now.

Cheers,
Paul

[elanjacobs]

Thanks that was fascinating. Terrific video, will be looking at rest of that numberphile site for a while. anybody gets this far without watching the video then go back and do it.

I've slowly worked my way through the whole lot of them and, on the whole, they're all fascinating. The same guy has channels on physics and chemistry as well, called Sixty Symbols and Periodic Videos respectively, for those interested.

[pmcgee]

I've slowly worked my way through the whole lot of them and, on the whole, they're all fascinating. The same guy has channels on physics and chemistry as well, called Sixty Symbols and Periodic Videos respectively, for those interested.

And he's an aussie from ... South Australia (I think). Brady Haran.