geometry

[Phil Pascoe]

Is there a way of dividing a circle into 5 and 7? I can't recall its ever cropping up. I'm making a dividing "table" to pattern and inlay turnery. I've used my indexing on the lathe to get 24 points, but for the purposes of aethetics I would like 5 and 7. i'm taking photos ... on a camera :shock: and if all goes to plan I'll do a WIP

 

[AndyT]

This might do - from 'The Modern Carpenter and Joiner and Cabinet Maker' volume III

 

[Random Orbital Bob]

Also I seem to recall from schoolboy maths if you set your compass to 1/5 the circumference and place the point anywhere on the circumference you can scribe an arc that bisects the circumference. Then move point to that bisected point and repeat until you have 5 equidistant points to which you draw in the straight lines. Voila, the sign of the devil!

But I'm sat outside hospital waiting for my Missus so can't try it and therefore it may be complete and utter rubbish! Always here to help

 

[JSW]

Use a protractor, 360 degrees divided by 5 = 72 degrees, or divided by 7 = 51.42 degrees, or am I missing something?

 

[NickWelford]

Printable 360 degree protractor

 

[NickWelford]

Or this

 

[Phil Pascoe]

Use a protractor, 360 degrees divided by 5 = 72 degrees, or divided by 7 = 51.42 degrees, or am I missing something?

No, you're not missing anything. I was wondering if someone would come up with a way of doing it with a compass/dividers that is so simple I'd always missed it. I might have to buy a protractor, although accurately marking off 51.42 degrees might be a little hit or miss.

 

[JSW]

Just print out the 360 degree protractor Nick linked to, pritstick it to your workpiece, strike thru the lines for whatever angles you need, remove template, join lines back up and then draw any size circle you want, already bisected.

 

[AndyT]

Phil, I've been reading up on this and feel I ought to warn you about not taking too many shortcuts...

According to the Science Museum,

"Eighteenth-century craftsmen marked out the degree scales on scientific instruments with great accuracy, using basic geometrical principles, compasses and hand tools. However, this was a time-consuming task."

until clever people like Jesse Ramsden invented the Dividing Engine to automate the job. So this is what you need to make:

then you can make a division plate with rings of 360, 192, 144, 120, 112 and 96 holes as described by Holtzapffel here.

It does look like an enjoyable project. When's the wip going to be ready? :lol: :lol:

 

[Bm101]

51.42 degrees. Nailed it! I just need to learn to cut at 90 degrees now.

God bless Moore and Wright ebay joblots! 8)

Andy, I'm pretty sure that's a time machine mate.

 

[Jacob]

Use a protractor, 360 degrees divided by 5 = 72 degrees, or divided by 7 = 51.42 degrees, or am I missing something?

No, you're not missing anything. I was wondering if someone would come up with a way of doing it with a compass/dividers that is so simple I'd always missed it. I might have to buy a protractor, although accurately marking off 51.42 degrees might be a little hit or miss.

Dividers are called dividers for a good reason - they are for accurate division.
To divide a line (or the circumference of a circle) by 5 - stride out an approximation of the division you want, as close as you can judge.
There will be an error, plus or minus (unless you hit it spot on first go).
Adjust the dividers to a point +/- 1/5 of this error (as close as you can judge) and try again. This will be closer. If not close enough carry on and divide the reduced error (as close as you can judge).
This is amazingly accurate for all practical purposes i.e. error will be at the limit of what you can see.
It's also the origin of the duodecimal system: it's easier to divide (and/or subdivide) a line by 2,3,4, and more practically useful, rather than than 5
A craftsman could easily mark out his own yard stick accurately in feet, inches, fractions. It'd be his own yard (non standard) but fully functional for his own project in hand.
The decimal system was based on crude counting of digits (fingers and toes) hence 5, 10, 20. The later duodecimal system was more sophisticated and met the needs of astronomers, navigators, precision engineers etc.

 

[finneyb]

I'm not fully understanding why you want to divide the circle, but if its for segmented turning why not use this http://www.woodturnersresource.com/extr ... gmentcalc/ to give you the internal angle values ?

Brian

 

[Bm101]

Use a protractor, 360 degrees divided by 5 = 72 degrees, or divided by 7 = 51.42 degrees, or am I missing something?

A craftsman could easily mark out his own yard stick accurately in feet, inches, fractions. It'd be his own yard (non standard) but fully functional for his own project in hand.

Yeh but not just anyone can cut a straight line at 3 or 4 different angles while maintaining the deception that it is to all intents and purpose a line of some variety. It takes hidden talent to do that. Very deeply hidden talent.

 

[Jacob]

......
A craftsman could easily mark out his own yard stick accurately in feet, inches, fractions. It'd be his own yard (non standard) but fully functional for his own project in hand.

Yeh but not just anyone can cut a straight line at 3 or 4 different angles while maintaining the deception that it is to all intents and purpose a line of some variety. It takes hidden talent to do that. Very deeply hidden talent.

Not sure what you mean?

 

[Bm101]

Ah, just mocking my saw technique Jacob. :wink:

 

[transatlantic]

I wonder if it would be easier to instead use a circle cutting jig to create a perfect circle of the intended radius.

Calculate the edge length using something like this to punch in your radius and number of edges http://planetcalc.com/92/

Pick any point on the circumference for your first point. Then use a ruler to measure out the edge length calculated above intersecting the appropiate part of the circumference. Repeat.

Seems as though it could be more accurate than trying to use a protractor, at least for big things

 

[AndyT]

Phil, if you want a method just using compasses and rule, this alternative from later in the same book might do for the pentagon. It avoids the step of dividing a straight line into five parts and looks a bit simpler.

Not much help for the division into seven though.

 

[Retire2004]

Hi phil.p
Try this one: www.cgtk.co.uk/metalwork/reference/divider
Not sure how to do the link

Regards
Tudor

 

[Phil Pascoe]

Brilliant - I think that'll do. In the fullness of time all will be revealed. I haven't a large enough dividers with a screw attachment, and huge one was proving to difficult to set finely enough although I'd probably get there in the end. I'm trying to keep it as accurate as I possibly can - I'm trying to make life easier, not harder.
Thanks, everyone, some interesting comments and ideas.

 

[Jacob]

Brilliant - I think that'll do. In the fullness of time all will be revealed. I haven't a large enough dividers with a screw attachment, and huge one was proving to difficult to set finely enough although I'd probably get there in the end. I'm trying to keep it as accurate as I possibly can - I'm trying to make life easier, not harder.
Thanks, everyone, some interesting comments and ideas.

You can replace dividers (or compasses) with a lath - pin at one end, notches at the other, new notches by way of adjustment.
Dividers work just as well around a circle as along a straight line