Text 11 Stones and beads
At some point you will want to incorporate stones or beads into your work. Stones add color, depth, and focus to a piece of jewelry. There are many ways of setting stones into metal. The intention of any setting technique is to show a stone to its best advantage. It may be a very simple rub-over setting or a detailed claw setting, but in all cases a setting is made to fit an individual stone.
Stones are available in a huge variety of colors and sizes, and they can range from being relatively affordable to priceless. The appearance of any stone depends on how it has been cut to reflect light.
Cuts of stones
Cuts vary, depending on the type of stone and the desired effect. Variations on the brilliant cut, for example, are designed to let light reflect through the stone. Fancy cuts are used to retain weight or sometimes to disguise flaws.
Stone shapes
Cabochon: Cabochon stones usually have a flat—or nearly flat—base and a smooth domed top. They may be any shape, but oval or round cabochons are most common. To hold them into a setting, a small collar, or "bezel," is made that fits neatly around the outside edge of the stone and is gradually coaxed over and down onto it.
Faceted: Faceted stones have many flat angled surfaces that combine to reflect light in an eye-catching way. Precious stones, such as diamonds, sapphires, emeralds, rubies, spinels, and topaz are usually given a faceted cut. They can be all sorts of different shapes, but the cut most often given to any of the shapes is "standard brilliant cut."
Buying stones
There is such a fantastic array of beautiful stones and beads available that it can be difficult to know where and what to buy. Many large towns and cities have a dedicated bead store where you will find individual beads and different strings of semiprecious beads that can be simply made up into necklaces. There is also a growing number of gem shows where individual stone importers and dealers show their wares, and these can be found in many different locations around the country. As well as a massive array of strung beads to choose from, you will find some lovely cabochon and faceted stones. Internet sales are amazingly popular, but at first, it is advisable to buy just one stone or a single string of beads to minimize risk until you find a dealer you can trust.
Carats
Stones are usually sold by weight, which is measured in carats. (You may see it spelled with a "k" rather than a "c".) There are 100 points in a carat, so if you know that a stone is a "10-pointer," that means it weighs one tenth of a carat. To determine the carat weight of a stone:
• Weigh the stone in grams
• Multiply the weight in grams by five; this is the number of carats
To find the cost of the stone, multiply the number of carats by the cost per carat of the stone. Some stones are sold per item, but this usually applies to cheaper stones such as turquoise, quartz, and hematite.
Quality
Generally speaking, the clearer the stone, the better the quality. However, remember that very clear flawless stones may have been manufactured and heat-treated—which is fine, as long as you know that is what they are. More expensive stones such as rubies and emeralds may have been enhanced by heat, treated with lasers, or injected to give them a better color. Unless stones are very expensive they are unlikely to be totally unflawed; and if the color looks too good to be true it probably is. Most stone suppliers have a showroom, so contact them first and ask to go and see what they have in stock. Pick out one or two things that you really like and can afford, and don't feel pushed into buying more then you want.
Opals
Opals sometimes have a dark backing applied to them, to enhance the colors of the stone; these are called doublets or triplets. Opals without any backing usually look quite milky (unless they are orange fire opals or black opals).
Turquoise
Turquoise is very soft; it breaks easily if there is too much pressure put on it while setting or stringing. The most valuable turquoise is rather muddy green one, with black lines running randomly through it (the matrix).
Stars and cat's eyes
Stars generally appear in sapphires and rubies. If they are held in the light you should see strong thin lines radiating out from the center in the shape of a star. If the stone is very clear as well as having a star, it will be expensive. If the stone is rather opaque with a star, it is usually less expensive. Cat's-eyes appear as a thin line right across the stone and seem to move with the light. They add value to it. Both cat's-eyes and stars only appear in cabochon stones.
Tourmalines
Tourmalines are very popular stones. They come in a fantastic range of colors, from blue, to turquoise blue, gray, dark green, light green, pink, and yellowish. Sometimes two or three of those colors appear in the same stone. A clear dark green or pink stone can be very expensive.
Appendix
Appendix 1
Jeweler's Dictionary
A
Anneal: A process of heating metal which has become compact and brittle. The heating removes the brittleness and renders the metal soft and malleable, so it can be worked.
Argentium Silver: is a modern sterling silver alloy which modifies the traditional sterling silver alloy (92.5% silver + 7.5% copper) by replacing some of the copper with the metalloid germanium. Argentium Silver is the result of research by Peter Johns at the School of Art & Design, Middlesex University. The project began in 1990 with research on the effects of germanium additions to silver alloys.
Asteria: Asteriated or asterism refer to a property possessed by some gem stones when cut cabochon or when viewed in transmitted light, of reflecting the light as a star, or surrounding the light source with radiating rays.
Automatic Center Punch: Manually powered punch used for marking locations on metal for accurate drilling of holes.
B
Bail: A finding, connected to pendants or stones worn as pendants to accommodate a chain, cord or thong.
Base Metal: Any non precious metal.
Basket Setting: A fancy setting of various shapes with numerous side piercings that provide a basket work or lacy appearance.
Bead Setting: A variety of gemstone setting in which the clamps over the edge of the stone are formed by pressing into the metal a punch which has a hemispherical hollow, which forms the bead.
Bearings: the groove or shoulder in which a stone is fitted in a piece of jewelry.
Bench Jeweler: an artisan who utilizes a combination of jewelry-making skills to make and repair jewelry. The jewelry making arts can be subdivided into a very great many categories of specialized skills. Some of the more common skills that a bench jeweler might employ include goldsmithing, stone setting, engraving, fabrication, Wax Carving, lost-wax casting, electroplating, forging, and polishing.
Bezel: A continuous groove o a form to fit a stone in a piece of jewelry, with metal at top of groove burnished over the edge of the stone to form a setting.
Binding Wire: The soft iron wire used for binding together parts of jewelry while being soldered.
Bobbing: Sand bobbing is a process used for polishing soft metals and removing scratches, pit marks and other imperfections without dragging the metal.
Bobbing Compound: A tripoli type compound used as a fine abrasive before polishing.
Brass: An alloy metal composed of various proportions of copper and zinc- an average formula is 65 parts copper and 35 parts zinc.
Brilliant: A type of cutting, used especially on diamonds with 58 facets, and also, now used as a synonym for a brilliant-cut diamond.
Burnisher: A tool for polishing metal by burnishing (by rubbing and pressing it with the steel).
Burnout Furnace: A gas or electrically powered furnace used to eliminate, by burning out, the wax from investment molds.
Bur: A milling cutter for forming a seat for a stone in setting a piece of jewelry, for removal of metal in hard to reach areas and cutting special shapes.
C
Cadmium: An elemental metal used as an alloy in gold solders to promote easy flowing under heat.
Caliper: Usually a measuring tool with adjustable jaws that embrace the object being measured.
Carat: A unit of weight for gemstones.
Carving Wax: Extremely hard wax used for carving, drilling, sawing and filing in making wax models.
Casting: A process for forming an object by pouring melted metal into a hollow mold; often used for duplicating a piece of jewelry, using the original piece as a pattern for making the mold.
Casting Wax: Wax especially formulated for used as patterns for casting.
Centrifugal Casting: A method of making small metal castings used in jewelry shops. Molds filled with melted metal, are whirled by machinery so that centrifugal force crowds metal into the smallest spaces producing work sharp in details.
Channel Setting: A type of setting often used in mounting a number of small stones of uniform size in a row, as in a diamond wedding ring.
Chasing: A highly skilled and ancient art of decorating metal with figures or ornamental patterns, which may be either raised or indented.
Cloisonné: a type of decoration for enameled metal-ware, consisting of narrow thin strips of metal soldered in the form of designs to the surface of a piece of ware, the spaces enclosed by the little metal walls filled with different colors of enamel.
Copper: A reddish metallic element used in the pure form as a conductor of electricity, also in enamel dial bases, as an alloying element in sterling silver, karat golds, brasses, bell metals, bronzes and other alloys.
Crucible: A container made of refractory material in which metals are melted. They are made in sizes and shapes to suit the purposes to which they are put.
Cuttlefish Bone: Dried porous bone used for quickly making molds for casting small pieces of jewelry.
D
Dapping-die: An iron cube with a variety of concave sinks on its faces, used with corresponding punches to produce cup-shaped forms in sheet metal.
Denatured Alcohol: Alcohol with small proportion of chemicals added to render it unfit for drinking; used for cleaning.
Diamond: From Old French diamant, which derives from the Latin adamas, "unyielding". A mineral composed of pure carbon, the hardest of all known substances and a valued gem found in many colors.
Diamond Tweezers: Tweezers with rounded ends, corrugated tips and rather a weak spring to hold diamonds and other stones.
Dividers: Tool for drawing circles, or spacing divisions of length, formed of two arms pivoted adjustably together at one of their ends, the other ends pointed for the uses stated.
Draw-Plate: A steel plate with graduated holes, through which metals may be pulled or drawn to form wire.
Drill: A boring tool for producing holes.
E
Electroplating: Process of covering metal articles with a film of other metals. The article is immersed in a chemical solution; electric current flows from the Anode (a piece of metal) to the Cathode, depositing the metal by electrolysis.
Emery Paper: Stiff paper coated with various grades of emery grains glued on, used for grinding and polishing.
Enamel: A medium used for decorative and other work on jewelry.
Engraving: The art of cutting designs in any substance; in the jewelry trades, particularly made of the precious metals.
Etching: A process for producing designs on metal by using acid, the design is scratched through a coating of wax or varnish on the article, exposing the surfaces of the metal, and acid is applied to eat into the metal to form the design in etching.
F
File: A hand tool for cutting metal, to shape it. Usually made of steel,, with teeth cut by chisel to cover its surface, then hardened.
Findings: Standardized parts of jewelry marketed for use in manufacturing and repair work, such as pin tongs, joints, settings, etc.
Fire Scale:Discoloration of copper alloys when heated in air. In the case of sterling silver this discoloration is extremely difficult to remove.
Flux: A substance used to promote fusion by preventing oxidation at the point of soldering, thus enabling the solder to flow.
G
Gauge: A measuring device for determining diameters, thickness, height, etc.
Gem: A stone cut and polished for use in jewelry, which fulfills the requirements for beauty, durability and rarity.
Gemstone: A naturally occurring mineral found in the rocks of the earth, the chemical composition and internal atomic structure of which make it suitable for jewelry use: color, clarity, hardness, rarity and availability.
Gold:a chemical element with the symbol Au (from its Latin name aurum) and atomic number 79. It is a highly sought-after precious metal which has been used as money, a store of value and in jewelry since the beginning of recorded history. The metal occurs as nuggets or grains in rocks, underground "veins" and in alluvial deposits. It is one of the coinage metals. Gold is dense, soft, shiny and the most malleable and ductile substance known. Pure gold has a bright yellow color traditionally considered attractive.
Goldsmith: a metalworker who specializes in working with gold and other precious metals, usually in modern times to make jewelry. Historically goldsmiths have also made flatware, platters, goblets, decorative and serviceable utensils, and ceremonial or religious items, but the rising prices of precious metals have curtailed the making of such items to a large degree. Goldsmiths must be skilled in forming metal through filing, soldering, sawing, forging, casting, and polishing metal. Traditionally, these skills had been passed along through apprenticeships, however, more recently Jewelry Arts Schools specializing solely in teaching goldsmithing and a multitude of skills falling under the jewelry arts umbrella are available.
Granulation: An ancient jewelry art by which small gold particles adhere to the surface without evidence of solder.
H
Heated Stone: A stone that has been treated by heat to change its color at the mine or after cutting; in electric ovens with stones embedded in sand.
Hinge-joint: One of the three or more pieces of metal tubing forming with a pin a hinge for a locket, etc.
I
Ingot Molds: A mold usually made of iron and with adjustable walls to produce a variety of sizes of cast metal bars or ingots.
Investment: A refractory material used to surround a disposable pattern, as of wax, and act as a mold for receiving metal which fills the cavities of the eliminated pattern.
J
Jeweler: A merchant who sells diamonds, other gemstones and jewelry.
Jewelry: Articles of personal adornment such as rings, bracelets and necklaces, made of precious or non-precious materials, often set with natural, synthetic or imitation stones, or natural, cultured or imitation pearls.
Journeyman: a workman who has completed learning his trade, and is fit to hold a job as a full-fledged workman as a jeweler; to differentiate from an apprentice, student, or other workman who cannot do all the work.
Jump Ring: An item of jewelry findings. Plain rings of graded sizes and various metals, round or oval, the ends of wire meeting but not soldered together, for attaching parts of jewelry together, in manufacturing assembling, or repairing.
K
Karat: One twenty-fourth part by weight of the metallic element gold in an alloy. Pure or fine gold is 24 karats.
Karat Gold: A gold alloy of not less than 10 karat fineness, preceded by the karat fineness of the alloy, such as 14 karat gold or 14 K. gold.
L
Lacquer: a synthetic varnish in which resins asphalt or cellulose acetate serves as bases.
Lapidary: A person who cuts and polishes gems except, in trade usage, diamonds.
Laser: Term under which an optical maser has become known. An acronym for Light Amplification by Stimulated Emission of Radiation. Using a fluorescent gas or doped solid, such as a synthetic ruby crystal, it produces a powerful, intensely hot, straight-line beam of light of every restricted diameter, capable of burning its way through solid substances.
Laser Welding: A soldering technique used to join multiple pieces of metal through the use of a laser. The beam provides a concentrated heat source, allowing for narrow, deep welds and high welding rates. The process is frequently used in high volume applications.
Lost Cast Waxing: A process of casting whereby a wax model is encased in an investment similar to plastic, the investment is agitated mechanically or put into a vacuum to remove air bubbles and placed in an oven where the wax is burned off, leaving a cavity which is filled through an opening with molten metal.
Loupe: magnifying glass worn over one eye; with a single lens or a system of lenses for greater magnifying power.
M
Mallet: A hammer with a heavy head made of non metallic material, used for cold forging operations on soft metals, to avoid denting the work as would be done by a steel hammer.
Mandrel: A steel rod slightly tapered, used as an anvil for forming rings by blows with the rawhide mallet.
Metallurgy: the art and science of extracting metals from their ores and preparing them for use by the manufacturer, who fashions them into finished articles.
Mill: A pair of steel rolls to rotate opposite to each other, used in jewelry shops for reducing thickness of bars of metals.
Moh's Scale: A scale of relative hardness for use in testing minerals.
Mold: A flexible rubber form into which casting wax is forced to make an expendable pattern.
Mounting: A piece of jewelry made for stones, complete except for the setting of the stones.
N
Nickel Silver: Or German silver. So called because of some color resemblance to the precious white metal; not because of any silver content.
Noble Metals: Metals that are permanent in air, showing no tendency to oxidation under ordinary conditions.
O
Ounce Troy:A unit of Troy weight, long used for weighing precious metals. The ounce contains 20 penny-weights each of 24 grains.
Oxidation: The forming of an oxide, as the copper in sterling silver or a karat gold alloy combining, through heat, with oxygen and forming a copper oxide.
P
Pennyweight: A unit of Troy weight, used for weighing precious metals.
Pickle: A mixture of about nine parts water and one part sulfuric acid, used by jewelers for cleaning gold and silver work after soldering.
Pitch: A black substance obtained from the distillation of coal tar.
Platinum: A white metallic element, the most important member of the platinum group; named platina, meaning "silver of little value," in 1735 by Spanish explorers of Colombia.
Platinum Group: The six metallic elements, platinum, palladium, iridium, osmium, rhodium and ruthenium.
Pliers: Two crossed metal limbs, hinged near their extremities, these forming jaws to grasp objects, bend or cut wire.
Polishing: The final series of operations in the production of jewelry. After a piece is made it is smoothened progressively from filing to successively-finer emery paper to buffs charged with Tripoli and rouge.
Precious Metals: metals which are prized because of chemical and physical properties desirable in jewelry. These metals are gold, silver and the six metals of the platinum group.
Precious Stones: One of three categories of natural gemstones. The most valuable, as distinguished from semi-precious and decorative. These are: diamonds, rubies, emeralds, sapphires and pearls.
Prong: One of several wires or claws used to fasten and hold a stone in place.
Q
Quartz: Silicon dioxide, one of the commonest of all minerals. It crystallizes in a the hexagonal system.
R
Rectifier: a device that changes alternating current to direct current.
Repoussé: A kind of decorative work on metal objects, in which a design is formed by punching or pressing portions of metal out from the inside or back of the object.
Riveting: fastening parts together by pins through holes in parts, the ends of pins hammered into form of heads larger than the holes.
S
Sanding: The process after filing, in which the file marks are removed from the piece.
Sawblades: for use in the jewelers'sawframes; narrow, flexible steel strips with teeth cut metal on one edge, fastened at both ends to clamps of the sawframe, which stretches the blade at considerable tension in use.
Sawframe: An adjustable frame in which a sawblade is clamped at both ends.
Scribe: A pointed steel rod in handle used for laying out outlines of work for sawing.
Semi-precious: The second and largest of the three categories into which gemstones have been divided by traditional usage. These are tanzanite, red tourmaline, green garnet, golden topaz, amethyst and chrysoprase.
Setting: The part of a piece of jewelry into which a stone or other gem is directly set.
Silver: is a chemical element with the symbol "Ag" (Latin: argentum, from the Ancient Greek - argentos, gen. - argeeis, "white, shining") and atomic number 47. A soft, white, lustrous transition metal, it has the highest electrical conductivity of any element and the highest thermal conductivity of any metal. It occurs as a pure free metal (native silver) and alloyed with gold (electrum), as well as in various minerals, such as argentite and chlorargyrite. Most silver is produced as a by-product of copper, gold, lead, and zinc mining.
Silversmith: is a person who works primarily making objects in solid silver; historically the training and guild organization of goldsmiths included silversmiths as well, and the two crafts remain largely overlapping. Unlike blacksmiths, silversmiths do not shape the metal while it is red-hot but instead, work it at room temperature with gentle and carefully placed hammer blows. The essence of silversmithing is to take a flat piece of metal and by means of different hammers, stakes and other simple tools, to transform it into an useful object.
Soldering: Uniting pieces of metal by melting between them another kind of metal.
Square: A metal instrument with one bar at a right angle to another, for testing the alignment of work.
T
Tweezers: Tools for quick handling of small pieces in watch and jewelry work; differing from pliers in having jaws on a pair of springs, fastened together at one end.
V
Vacuum Casting: A process whereby a coating metal is deposited on a substance by volatilization in a vacuum.
W
White Gold: Usually, an alloy of gold, copper, nickel and zinc.
Y
Yellow Gold: See Gold
Appendix 2
Conversion charts | |||||||||
METAL THICKNESSES | QUICK REFERENCE MM/GAUGE SIZES | ||||||||
Precise metric and imperial gauge conversions | |||||||||
B&S guage | mm | inches | mm | nearest B&S gauge | |||||
6.54 | 0.258 | 3.00 | |||||||
5.19 | 0.204 | 2.50 | |||||||
4.11 | 0.162 | 2.00 | |||||||
3.26 | 0.129 | 1.50 | |||||||
2.59 | 0.102 | 1.25 | |||||||
2.05 | 0.081 | 1.00 | |||||||
1.63 | 0.064 | 0.75 | |||||||
1.29 | 0.051 | 0.64 | |||||||
1.02 | 0.040 | 0.50 | |||||||
0.81 | 0.032 | ||||||||
0.64 | 0.025 | ||||||||
0.51 | 0.020 | ||||||||
0.40 | 0.015 | ||||||||
0.33 | 0.013 | ||||||||
0.25 | 0.010 | ||||||||
0.20 | 0.008 | ||||||||
0.16 | 0.006 | ||||||||
0.13 | 0.005 | ||||||||
RING SIZES | |||||||||||||||||||||||||||||||||||||
US | UK | Europe | mm | inches | US | UK | Europe | mm | inches | US | UK | Europe | mm | inches | |||||||||||||||||||||||
1/2 | A | 37.83 | 1.490 | 1 1/2 | 49.20 | 1.938 | 9 1/2 | T | 61.13 | 2.408 | |||||||||||||||||||||||||||
3/4 | A 1/2 | 38.42 | 1.514 | 5 1/4 | K | 49.80 | 1.962 | 9 3/4 | T 1/2 | 61.77 | 2.434 | ||||||||||||||||||||||||||
B | 39.02 | 1.537 | 5 1/2 | K 1/2 | 50.39 | 1.986 | U | 62.40 | 2.459 | ||||||||||||||||||||||||||||
1 1/4 | B 1/2 | 39.62 | 1.561 | 5 3/4 | L | 50.99 | 2.009 | 10 1/4 | U 1/2 | 63.04 | 2.484 | ||||||||||||||||||||||||||
1 1/2 | C | 40.22 | 1.585 | L 1/2 | 51.59 | 2.033 | 10 1/2 | V | 63.68 | 2.509 | |||||||||||||||||||||||||||
1 3/4 | C 1/2 | 40.82 | 1.608 | 6 1/4 | M | 52.19 | 2.056 | 10 3/4 | V 1/2 | 64.32 | 2.534 | ||||||||||||||||||||||||||
D | 41.42 | 1.632 | 6 1/2 | M 1/2 | 52.79 | 2.080 | W | 64.88 | 2.556 | ||||||||||||||||||||||||||||
2 1/4 | D 1/2 | 42.02 | 1.655 | 6 3/4 | N | 53.47 | 2.107 | 11 1/4 | W 1/2 | 65.48 | 2.580 | ||||||||||||||||||||||||||
2 1/2 | E | 42.61 | 1.679 | N 1/2 | 54.10 | 2.132 | 11 1/2 | X | 66.07 | 2.603 | |||||||||||||||||||||||||||
2 3/4 | E 1/2 | 43.21 | 1.703 | O | 54.74 | 2.157 | 11 3/4 | X 1/2 | 66.67 | 2.627 | |||||||||||||||||||||||||||
F | 43.81 | 1.726 | 7 1/4 | O 1/2 | 55.38 | 2.182 | Y | 67.27 | 2.650 | ||||||||||||||||||||||||||||
F 1/2 | 44.41 | 1.750 | 7 1/2 | P | 56.02 | 2.207 | 12 1/4 | Y 1/2 | 67.87 | 2.674 | |||||||||||||||||||||||||||
3 1/4 | G | 45.01 | 1.773 | 7 3/4 | P 1/2 | 56.66 | 2.232 | 12 1/2 | Z | 68.47 | 2.680 | ||||||||||||||||||||||||||
3 1/2 | G 1/2 | 45.61 | 1.797 | Q | 57.30 | 2.257 | |||||||||||||||||||||||||||||||
3 3/4 | H | 46.20 | 1.820 | 8 1/4 | Q 1/2 | 57.94 | 2.283 | ||||||||||||||||||||||||||||||
H 1/2 | 46.80 | 1.844 | 8 1/2 | R | 58.57 | 2.308 | |||||||||||||||||||||||||||||||
4 1/4 | I | 47.40 | 1.868 | 8 3/4 | R 1/2 | 59.21 | 2.333 | ||||||||||||||||||||||||||||||
4 1/2 | 1 1/2 | 48.00 | 1.891 | S | 59.85 | 2.358 | |||||||||||||||||||||||||||||||
4 3/4 | J | 48.60 | 1.915 | 9 1/4 | S 1/2 | 60.49 | 2.383 | ||||||||||||||||||||||||||||||
Appendix 3 Mathematical signs and symbols | |||||||||||||||||||||||||||||||||||||
+ | plus (sign of addition) | - | minus (sign of subtraction) | ||||||||||||||||||||||||||||||||||
+ | positive (sign of polarity) | - | negative (sign of polarity) | ||||||||||||||||||||||||||||||||||
+ | plus or minus | ′ | minutes | ||||||||||||||||||||||||||||||||||
x | times, by (multiplication sign) | ″ | seconds | ||||||||||||||||||||||||||||||||||
• | multiplied by | dx | differential of x | ||||||||||||||||||||||||||||||||||
÷ | sign of division | Δ | delta, difference | ||||||||||||||||||||||||||||||||||
/ | divided by | Δx | increment of x | ||||||||||||||||||||||||||||||||||
: | ratio sign, divided by, is to | ∂u/∂x | partial derivative of u | ||||||||||||||||||||||||||||||||||
:: | equals, as (proportion) | with respect to x | |||||||||||||||||||||||||||||||||||
< | less than | ∫ | integral of | ||||||||||||||||||||||||||||||||||
> | greater than | Σ | sigma, summation of | ||||||||||||||||||||||||||||||||||
≪ | much less than | f(x), F(x) | functions of x | ||||||||||||||||||||||||||||||||||
≫ | much greater than | ∇ | del or nabla, vector | ||||||||||||||||||||||||||||||||||
= | equals | differential operator | |||||||||||||||||||||||||||||||||||
~ | similar to | ∇2 | Laplacian operator | ||||||||||||||||||||||||||||||||||
≈ | approximately equals | L | Laplace operational | ||||||||||||||||||||||||||||||||||
≊ | approximately equals, congruent | symbol | |||||||||||||||||||||||||||||||||||
< | equal to or less than | 4! | factorial 4 = 1 x 2 x 3 x 4 | ||||||||||||||||||||||||||||||||||
> | equal to or greater than | |x| | absolute value of x | ||||||||||||||||||||||||||||||||||
ǂ ≠ | not equal to | ẋ | first derivative of x | ||||||||||||||||||||||||||||||||||
→ ≐ | approaches | with respect of time | |||||||||||||||||||||||||||||||||||
α | varies as | ẍ | second derivative of | ||||||||||||||||||||||||||||||||||
∞ | infinity | x with respect of time | |||||||||||||||||||||||||||||||||||
√ | square root of | A x B | vector x produkt; | ||||||||||||||||||||||||||||||||||
∛ | cube root of | magnitude of A | |||||||||||||||||||||||||||||||||||
∴ | therefore | times magnitude of B | |||||||||||||||||||||||||||||||||||
║ | parallel to | times sin of the angle | |||||||||||||||||||||||||||||||||||
(), [], | parentheses, | from A to B | |||||||||||||||||||||||||||||||||||
{ } | brackets and braces. | A • B | scalar product of A and | ||||||||||||||||||||||||||||||||||
Quantities enclosed | B; magnitude of A times | ||||||||||||||||||||||||||||||||||||
by them to be taken | magnitude of B times | ||||||||||||||||||||||||||||||||||||
together in multiplying, | cosine of the angle from | ||||||||||||||||||||||||||||||||||||
dividing, ect. | A to B | ||||||||||||||||||||||||||||||||||||
∠ | angle | A • B | Cartesian product of | ||||||||||||||||||||||||||||||||||
° | degrees | set A and set B | |||||||||||||||||||||||||||||||||||
Appendix 4