PDA

View Full Version : Pumpkin Pie.



Dennis
04-02-2014, 11:29 AM
For those of you who are at ease with the relationship of pi to the radius of a circle, or sphere, please don’t read on; you’ll only get cross.

For those who were away when it was discussed at school, or simply turned off by it, imagine a pumpkin, round as round. Now, if you know how fat it is at its fattest point, that is the diameter, often simply called d, to save breath.

If you are a jeweller, then sometime you will want to make a ring to fit this round thing snugly. How long a piece of metal will you need? Well if you measure all the way round, you are measuring the perimeter; let’s call it l for short. That’s meant to be an l as in length.

But if you know the value of d already, you don’t need to measure l at all. You can work it out on your calculator. No matter how big or small the diameter d, if you multiply it by 3.14, you will get the perimeter l, or the length of metal to make a ring.

The number used is a constant, either written as a fraction, twenty-two divided by seven, or as the Greek letter pi, like this: π. What is more you don’t have to remember the number, because Sharp make a cheap school calculator (EL-S50) with a π key. They are only about a fiver online.

So when you see a diagram with lots of letters and arrows, it is just waiting to have the real figures put in. But if you see a letter, for example d, multiplied by pi, or just written πd, then that will give you the length of a bezel for your stone, or the length of metal for a ring.

Now comes a slight difficulty, but don’t give up. Rings have a thickness and the thicker they are, the more it affects the outcome. So to get things right, you can add twice the thickness of metal to your result.

Finger rings are a special case, because the way they feel on the finger is also affected by how wide they are. Not to worry, this online calculator will take care of it.

Use upper case for English sizes: http://mordent.com/toolsapps/
Our Wallace has painstakingly written down all the results as a table, but I’m not sure how to access it. Perhaps someone can post that link here too. Dennis.

medusa
04-02-2014, 12:45 PM
yeah, but what always gets me is the… aspect ratio? If the circumference is say 10cm then what length do you cut if the wire is say 2mm thick or 4mm thick? That's what always bugs me and I can never work out.

CJ57
04-02-2014, 01:41 PM
In the first ever book I bought written by a couple of girls that were at ECA just after me it said

Measure the diameter from your chosen ring size on the gauge with a ruler
Multiply by pi and add twice the thickness of the metal. This will give you the exact length of wire or metal to cut

It seemed the easiest way for me once I'd remembered what pi was ! :)

caroleallen
04-02-2014, 01:44 PM
Switched off, sorry! I like Wallace's chart - tells me everything I need to know.

mizgeorge
04-02-2014, 01:48 PM
Wallace's lovely chart is in this thread: http://www.cooksongold.com/forum/showthread.php?t=5031

lorraineflee
04-02-2014, 02:22 PM
Thought someone might be interested in one of the puzzles I did for my grandson when he was 8 and wanting to learn more maths. I made a booklet of Starwars maths problems up on a week by week basis. This one was on circles!
5651

Wallace
04-02-2014, 03:17 PM
awww, thank you. Love you peeps!

so it is all in one place here you go. (as a reminder the thickness is across the top and ring size down the side).

5652

my original is in an excel spread sheet, which I can also share if anyone wants to PM their email

Anna Wales
04-02-2014, 03:42 PM
Used Wallace's chart today to make 2 rings and worked perfectly. The chart has a permanent place on the bench now.

medusa
04-02-2014, 06:19 PM
how could I get Wallace's chart to work for say bangles and collars? or should I use Caroline's suggestion of circumference + 2x metal thickness?

Dennis
04-02-2014, 07:25 PM
For say bangles and collars should I use Caroline's suggestion of circumference + 2x metal thickness? Please forgive the misquote, Liz.

That's the one to use I'm sure and your wearers will be quite happy.

Wallace
04-02-2014, 09:44 PM
5653

anyone want to try this for size? I have used the same methods for the rings... but up-scaled it for bangles and collars (I think??)

trialuser
04-02-2014, 11:18 PM
Hi Wallace, can I ask why you have chosen 3.147 as Pi?
It seems slightly odd, especially as you have gone to the level of 3 decimal places:)
Although it probably doesn't make any real difference in practice.

ps_bond
05-02-2014, 07:40 AM
Not sure I dare do any arithmetic after last time...
For a 17.93mm diameter, circumference using Pi @ 3.147 = 56.426 to 3 dec places
Using Pi @ 3.1415926535897932384626433832795 (copy & paste, Windows calculator) = 56.329 to 3 dec places.

0.172% error.

Measure with a micrometer. Mark with chalk. Cut with an axe.

Wallace
05-02-2014, 08:16 AM
Lol.... Was trying to help. Isn't pi 3.14? At 4 decimal places in mm, it was just the sumif function and being old, the pi was probably rhubarb or something ;). It worked on the original. But need to check to conversion when I get to my main PC. Thanks for checking. Back to the machine with my calc (works better than my working out the fx iin excel). No- one has to use anything, lol...thanks for checking it though.

trialuser
05-02-2014, 09:11 AM
Measure with a micrometer. Mark with chalk. Cut with an axe.

Lol - absolutely agree it makes no difference in real life.
I was just curious as Wallace had gone to the trouble of calculating to 3 decmal places and used a strange value for Pi.
I wondered if (s)he had picked up an anomaly in the original calculator that was needed to get it to work.
Wallace - it would be more usual to use 3.142 - but 3.147 is fine :-)
Thanks for doing it - I had been using the 'at the bench' one.
Martyn.

Didi
05-02-2014, 05:59 PM
Thanks to all. Prefer Apple pie to either pumpkin or rhubarb but love easy ways to get it right
Didi

metalsmith
05-02-2014, 07:23 PM
Perfection every time ... well almost
http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html

Dennis
05-02-2014, 09:00 PM
Great! beats measuring with binding wire.

Tabby66
05-02-2014, 10:30 PM
Aaaaaagh :(|:(|

Patstone
06-02-2014, 06:56 AM
Well I have used Wallace's chart and it works fine. The other day my 96 year old mum informed me that she had lots of necklaces and earrings now but could she have a ring to match a necklace and earrings that I made her for her birthday, so all I had to measure was a bit of string - worked fine, seems to be more accurate than my maths. Note to Dennis who kindly worked out some maths for me earlier, think I must have been asleep during maths lessons, can add up groceries in my head straight from the trolley/basket but anything more involved .........................