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.
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.