Maths and Beading

People often wonder how I can combine maths with beading. I actually find that my maths knowledge comes in very handy when beading. I recently designed a necklace which consisted of two concentric circles with some feature in between them. It was crucial to the way the necklace would hang, that the circles were the right length and had the correct curvature. It took quite a bit of calculation but I did manage to get it right. Fortunately bead weaving are fairly flexible and you do not need to do the calculations as accurately as in other fields of use of maths. Here are some guidelines of calculations that come in handy: Circumference of a Circle The circumference of a circle is a little more than 3 times its diameter. Therefore if you want to make a clasp by using a bead and make a loop with seed beads, times the diameter of the big bead by 3. Then divide your answer by the diameter of your seed beads. Add a few beads (about 2 or 3 depending on your size seed beads) to the answer and that should give you the number of beads you might need. To work out the curvature of a necklace, I usually estimate the circumference on the inside of the necklace to be 46cm. That gives me a diameter of about 15cm. If your pattern is 4cm broad, the diameter of your outside circle will be 15+2x (the width of your pattern) which in my example will be 15+2x4cm = 23cm. If you multiply this by 3 and add a bit on, you will have the length of the outside circumference. In my example it will be 23x3 = 69cm plus a bit. The exact calculation will bring you to 72cm. Remember to make allowance for the clasp which is about 3cm. Number of Beads Required I am sure that most bead weavers have at some stage experienced the frustration of running out of a specific type of bead they were using in a project. So how can you calculate the number of beads you will be needing for your project before you start? It is in fact a simple ratio calculation. First determine the length that you would like your project should be. I usually make my necklaces 46cm and bracelets 18cm. A normal toggle clasp uses about 3cm of that length. You will therefore need beads for about 43cm for a necklace and 15cm for a bracelet. If you are going to repeat the same pattern all the way around the project, you first need to work out the length of one repeat. Count the number of each type of bead you used in that single repeat of the pattern. Then calculate the number of repeats you will be doing by dividing 43cm or 15cm by the length of one repeat. Now multiply each type of bead used in one repeat by the total number of repeats you will be doing and this will give you the amount of beads of each type you will require. Note that 43 is a prime number and therefore cannot be divided without a remainder but 42 = 6x7 or 3x14 or 2x21. A pattern with any one of these digits will therefore repeat into a neat whole number. The 1cm that are missing can either be compensated for in the clasp part or a centre feature. Alternatively you can make a slightly longer necklace and use 44 = 4x11. For the bracelet you can use 3x5 = 15 or make it slightly larger and use 16 which gives 4x4 or 2x8.