text:
User talk:COMPATT~enwikibooks

What do you mean by "Computer basics"? r3m0t (cont) (talk) 00:08, 28 Feb 2004 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called COMPATT. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name COMPATT~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:04, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 04:44, 19 April 2015 (UTC)

title: User talk:COMPATT~enwikibooks


text:
Cookbook:Beef

| Basic foodstuffs | Meat and poultry

Beef is meat obtained from a bull, steer (castrated bull), or cow.

Production
There are two primary beef rearing methods. In some parts of the world (e.g. Australia and South America), beef cattle self-feed on grass and weeds while roaming around. This produces beef with fat deposits on the outsides of the beef cuts, where they can be removed before cooking. In the USA and some other countries, feedlot beef is much more common. These animals are confined to a small stockyard and fed primarily on grain. Feedlot animals produce beef which is tender, mild flavored, and marbled with large amounts of fat.

There is a special kind of beef produced in Japan called Kobe beef, which goes a step beyond feedlot production. Beef cattle of the Wagyu breed are hand-raised, fed on a diet of beer and quality grain, and given regular massages. This produces super-tender beef with lots of marbled fat. Kobe beef sells at a premium price because of the higher costs of feed and production.

After slaughter, beef must be allowed to rest and naturally tenderize before cooking. The tenderizing process may go a step further with dry aging, where beef is allowed to carefully putrefy under controlled cold and dry conditions. This concentrates its flavor and creates a more tender texture.

Characteristics
Beef is considered a red meat due to its higher levels of myoglobin. Very fresh meat that has not been exposed to oxygen will have a purpleish color. Once exposed to oxygen, the meat will turn bright red and eventually oxidize to brown after over a week. Beef fat is distributed both around individual cuts and within the muscle, the latter of which is called marbling. The more marbling, the more flavorful and tender the beef after cooking.

Beef is high in flavor compared to lighter meats, and it works well in many applications. It takes well to strong flavors. Beef from different parts of the animal will differ in flavor and texture. Generally, the more flavorful the meat, the less tender, and vice versa. Beef increases in tenderness the higher up it is on the animal, as the less-used muscles are the tenderest. Animal age also impacts the beef's tenderness, with younger animals producing more tender meat.

Grading
The USDA beef rating system encourages beef with high amounts of intramuscular fat by giving high scores to highly-marbled beef. From least marbled to most marbled, the grades are standard, select, choice, and prime. Subdivisions have recently been added; a "-" indicates a cut with less marbling while a "+" indicates more marbling. The letter grades refer to age of the animal, with "A" being for the youngest animals.

Cuts
After slaughter, beef is divided into several sections called cuts, which are then further subdivided into smaller sections for serving. Different regions have different standards for cuts, depending on local cuisines and regulatory bodies. In continental Europe, cuts tend to derive from individual muscles, and each cut will primarily consist of one muscle group—this results in consistency of flavor and texture across the cut. In the UK and North America, some cuts may consist of multiple muscle groups.

American Cuts
In the United States, beef is first divided into the following large "primal" cuts:

Brisket is a dense, tough cut from the chest of the animal. It is fatty and flavorful, and it is best suited for long slow cooking, such as slow roasting and braising.

Chuck is derived from the shoulder. It is somewhat fatty and tough but has good flavor. Some smaller cuts from the chuck are flat-iron steak, stew meat, chuck roast, chuck short ribs, and top blade steaks. It is also often used for ground beef.

Flank cuts are tough with a low fat content. It is suitable for braising. Cuts from the flank include flank steak and london broil. It is often recommended to cut flank across the grain to avoid excess chewiness.

The loin is a very tender cut of beef near the rear of the animal. The short loin is the most tender, and yields smaller cuts including tenderloin, filet mignon, strip steak and roast, T-bone steak, and porterhouse steak. The sirloin is slightly less tender than the loin and yields sirloin steak, tri-tip, ball tip, and sirloin flap, among others. If too lean, loin cuts can end up bland and lacking in flavor.

The plate comes from the abdomen. Its smaller cuts include skirt steak and short ribs.

Rib cuts are generally tender cuts from the middle of the animal, which often feature marbling. They include short ribs, rib-eye steak, rib-eye roast, cowboy steak, and back ribs.

The round is generally lean, tough, and inexpensive. It yields various roasts and some round steaks.

The shank comes from the leg of the animal. It is very tough and requires slow cooking, but it has excellent flavor.

Bones
Beef bones contribute a good deal of flavor, which is usually extracted in stocks and broths. Marrow bones are thick bones from the shank, and the soft fatty marrow in the center is nutrient dense and rich—it can be spread on foods.

Offal
Beef heart is somewhat springy. Other beef variety meats include the tongue, tripe from the stomach, various glands—particularly the pancreas and thyroid—referred to as sweetbreads, the brain, the liver, the kidneys, and the tender testicles of the bull commonly known as "calf fries", "prairie oysters", or "Rocky Mountain oysters."

Selection and storage
When choosing beef, look for bright red meat. It should smell fresh and have no off colors.

Use
The method used to cook beef often depends on the cut. Tougher pieces of beef with more connective tissue benefit from long, slow, moist cooking—this breaks down the collagen and produces a tender and melting final product. Tender cuts can be quickly cooked using dry heat, but they can easily become overcooked and will then suffer in texture.

Several Asian and European nationalities include beef blood in their cuisine—the British use it to make black pudding, and Filipinos use it to make a stew called dinuguan. Tongue is usually sliced for sandwiches.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Cookbook:Beef


text:
Cookbook talk:Beef

This module includes information copied from the Wikipedia article Beef. Below is the page history at the time the information was coppied:

* (cur) (last). . 14:18, 4 Feb 2004. . 128.172.154.59   * (cur) (last). . 06:15, 24 Dec 2003. . Karada (The perception of beef as potentially lethal caused significant damage to the UK beef industry. The sometimes over-zealous attempts to wipe out BSE in the UK by a kill-and-burn campaign, although ulti) * (cur) (last). . M 06:09, 24 Dec 2003. . Karada (casing) * (cur) (last). . 06:09, 24 Dec 2003. . Karada (Since then, a number of other countries have had outbreaks of BSE.) * (cur) (last). . 06:07, 24 Dec 2003. . Karada (casing) * (cur) (last). . 06:07, 24 Dec 2003. . Karada (Beef is taboo in a number of religions, fmt) * (cur) (last). . M 15:26, 9 Dec 2003. . Zoicon5 (spelling) * (cur) (last). . 11:16, 17 Oct 2003. . 62.253.96.42   * (cur) (last). . 04:35, 30 Sep 2003. . 218.110.223.3 (+ja) * (cur) (last). . 15:42, 31 Jul 2003. . 195.92.67.69 (BSE in the UK) * (cur) (last). . M 13:50, 31 Jul 2003. . Sannse (Disambiguating English) * (cur) (last). . 12:26, 26 Jul 2003. . 195.92.67.70 (link added) * (cur) (last). . 12:25, 26 Jul 2003. . 195.92.67.70 (Roast Beef added) * (cur) (last). . 06:03, 22 Aug 2002. . Heron (mad cow disease) * (cur) (last). . 13:40, 13 Jul 2002. . Roadrunner * (cur) (last). . 13:38, 13 Jul 2002. . Roadrunner * (cur) (last). . 07:43, 25 Feb 2002. . -- April (one more sentence... still stub.) * (cur) (last). . 10:17, 29 Jan 2002. . Vicki Rosenzweig (still very stubby) * (cur) (last). . M 09:35, 29 Jan 2002. . Clasqm (ultra-stub for the most wanted page)

Beef
beef is also a very important part of south african cultures and cuisine

And is used in many cultural traditions OFENTSE MO (discuss • contribs) 16:44, 1 July 2023 (UTC)

title: Cookbook talk:Beef


text:
Cookbook:Cabbage

The cabbage is an edible leafy vegetable.

Characteristics
Cabbages take the form of densely packed, round heads. The leaves are darker on the outside of the head and get paler all the way to the white core. The three primary varieties are green/white, savoy, and red/purple cabbage, and for the most part they are quite similar. Green and savoy cabbages are both green in color, though the leaves of savoy cabbages are more wrinkled than those of green cabbage. Red cabbage has the same texture as green cabbage, but its leaves are colored magenta instead of green

Selection and storage
When choosing cabbage heads, go for those that feel dense and firm, with as few wilted outer leaves as possible. They should have no rotted or slimy portions or browning. Ideally, the cores shouldn't seem dried out. Cabbages keep well in the fridge, wrapped in plastic. If they begin to discolor or get slimy, they should be discarded.

Use
Like all brassicas, cabbage is a potentially smelly vegetable that needs to be handled with care to avoid creating unpleasant odours and flavors. There are two ideal ways to cook cabbage: either very quickly (e.g. stir frying, blanching) or in a slow-cooked flavoursome dish. Cabbages may also be shredded and served raw as a salad or slaw, and dishes of fermented cabbage feature in various cultures. Because they are large, cabbage leaves are often used to wrap fillings, such as meat and rice.

To prepare cabbage for cooking, discard the outer leaves and tough core—the latter can be done more easily once the cabbage is quartered. From there, it can be cut up as desired for your dish. When cooking red cabbage, it can turn an unappetizing purple/grey color—cooking with an acid, such as vinegar, will keep it a nice red color.

title: Cookbook:Cabbage


text:
Cookbook talk:Cabbage

Moved from article - it goes somewhere but not under general 'cabbage' - Surprisingly, broccoli (var. italica), cauliflower (var. botrytis), kohlrabi (var. caulorapa), Brussels sprouts (var. gemmifera), Chinese kale or Chinese broccoli (var. alboglabra), broccolini (var. italica x alboglabra) and broccoflower (var. italica x botrytis) are varieties of the same plant species: Brassica oleracea. KJ 23:34, 29 Feb 2004 (UTC)

This module, or a version in the page history, contains text taken from the Wikipedia article Cabbage, used under the GFDL. The page history at the time the text was coppied was:

* (cur) (last). . 11:26, 24 Feb 2004. . Imc (internal link) * (cur) (last). . 20:17, 9 Feb 2004. . WormRunner (link to article about red cabbage as a pH indicator) * (cur) (last). . 13:37, 9 Feb 2004. . Kathy T (red cabbage juice is an indicator) * (cur) (last). . M 05:32, 1 Feb 2004. . Robbot (Andre Engels - robot Modifying:fr) * (cur) (last). . M 05:24, 22 Jan 2004. . Ahoerstemeier (how can there be an article about cabbage without the german interwiki link :-))   * (cur) (last) . . M 16:12, 21 Dec 2003 . . Montrealais    * (cur) (last) . . M 11:18, 25 Nov 2003 . . Rmhermen    * (cur) (last) . . 11:17, 25 Nov 2003 . . Rmhermen    * (cur) (last) . . 10:59, 25 Nov 2003 . . Rmhermen    * (cur) (last) . . 01:49, 13 Sep 2003 . . 218.221.232.123 (+ja)    * (cur) (last) . . M 14:35, 4 Sep 2003 . . Angela (Reverted to last edit by Marshman)    * (cur) (last) . . 14:30, 4 Sep 2003 . . 24.193.201.0    * (cur) (last) . . 01:10, 27 Aug 2003 . . Marshman (Copy edit; fix link >> dicots)    * (cur) (last) . . M 23:18, 8 Aug 2003 . . Jimfbleak (Pieridae)    * (cur) (last) . . 23:57, 3 May 2003 . . Zoe (photo)    * (cur) (last) . . M 15:12, 9 Feb 2003 . . Tarquin    * (cur) (last) . . M 15:09, 9 Feb 2003 . . Ellywa (sauerkraut is fermented (not pickled))    * (cur) (last). . M 07:23, 23 Jan 2003. . Frecklefoot (links) * (cur) (last). . 08:23, 5 Nov 2002. . Tarquin * (cur) (last). . M 06:54, 5 Nov 2002. . PierreAbbat (fr:) * (cur) (last). . M 04:54, 3 Oct 2002. . Andre Engels (nl:) * (cur) (last). . 04:33, 6 Jun 2002. . Vicki Rosenzweig (copyedit (spell out genus on first mention); notes on the food uses of cabbage) * (cur) (last). . 23:53, 5 Jun 2002. . 62.60.55.163 (*Cabbage=socially inept also) * (cur) (last). . M 22:37, 5 Jun 2002. . 213.105.87.146 (most wanted, stub)

title: Cookbook talk:Cabbage


text:
Cookbook:Flour

An ingredient used in many foods, flour is a fine powder made from cereal grain or other starchy food sources. It is most commonly made from wheat, but also corn, rye, barley and rice, amongst many other grasses and even non-grain plants.

Flour is always based on the presence of starches, which are complex carbohydrates.

Usually, the word "flour" used alone refers to wheat flour, which is one of the most important foods in European and American culture. Wheat flour is the main ingredient in most types of breads and pastries. Wheat is so widely used because of an important property: when wheat flour is mixed with water, a complex protein called gluten develops. The gluten development is what gives wheat dough an elastic structure that allows it to be worked in a variety of ways, and which allows the retention of gas bubbles in an intact structure, resulting in a sponge-like texture to the final product.

Wheat flour
The vast majority of today's flour consumption is of wheat flour.

Wheat varieties are typically known as hard or soft, depending on gluten content. Hard wheats are high in gluten, and soft wheats are low. Hard flour, or "bread" flour, is high in gluten and so forms a certain toughness which holds its shape well once baked. Soft flour is low in gluten and so results in a finer texture. Soft flour is usually divided into "cake" flour, which is the lowest in gluten, and "pastry" flour, which has slightly more gluten than cake flour.

In terms of the parts of the grain (the grass seed) used in flour -- the endosperm or starchy part, the oil-containing germ or protein part, and the bran or fiber part -- there are three general types of flour. "White" flour is made from the endosperm only. "Whole wheat" flour is made from the entire grain. A "germ" flour may also be made from the endosperm and germ, excluding the bran. The germ is sometimes sold by itself, as "wheatgerm".

 * Whole wheat flour (or wholemeal flour) is ground from the entire wheat kernel, including the germ and the bran.

 * Graham flour is a white flour with coarsely ground bran and wheatgerm mixed back in. It thus contains all three parts of the wheat kernel as whole wheat flour does, but it has a different texture.

 * Cake flour, is a milled, bleached flour containing a low amount of gluten (around 7%), and therefore bakes with a fine texture.

 * Pastry flour is slightly stronger (higher in gluten) than cake flour.

 * All-purpose flour, (known as plain flour in Europe) is a blended white flour containing a medium amount of gluten (around 10%).

 * Maida is a super-refined white flour used in Indian cuisine.

 * Self-rising flour (also called "Self-raising flour") is an all-purpose flour that has a leavening agent blended into it for convenience. One cup of self-rising flour can be replaced by one cup of all-purpose flour plus one teaspoon of baking powder and a pinch of salt.

Flours from other cereals

 * Corn flour is an ambiguous term that can mean cornstarch or finely ground cornmeal. Cornmeal which has been leached with lye is called corn masa (masa harina) and is used to make tamales and corn tortillas in Mexican cooking.

 * Atta is a popular flour used in South Asian cuisines, and is made by grinding whole wheat.

 * 100% rye flour is used to bake the traditional sourdough breads of Germany and Scandinavia.

 * Rice flour is of great importance in South-east Asian cuisines.

 * Sorghum flour (jowar) is used in many parts of Africa and South Asia.

 * Spelt flour is an alternative to wheat flour. Note: although some people with wheat allergies can tolerate spelt, other wheat-allergic patients have adverse reactions to spelt flour as well. Spelt also has less gluten than wheat, but it is not gluten-free.

 * Other grains (cereal and non-cereal) ground into flours include amaranth, barley, buckwheat, millet, oats, quinoa, teff, and triticale.

Flours Made of Legumes, Tubers, Pulses, Etc.

 * Chickpea flour (besan) is of great importance in Indian cuisine. Some other legumes ground for flour include soybeans, mung beans, yellow peas, urad dal, and fava beans.

 * Flour can also be made from various various roots and tubers, including arrowroot, cassava (manioc, tapioca), potatoes, sweet potatoes, taro root; and other non-grain foodstuffs.

Flours Made of Nuts

 * Almond Flour Finely ground blanched almonds (much finer than almond meal) is a flour sometimes used in cooking.
 * Coconut Flour Used often in gluten free cooking, coconut flour is considered a healthier alternative to wheat or grain flours.
 * Flour may also be made from most nuts using a food processor, including Brazil nut, Cashew, Pistachios, Macadamias, Hazelnuts, etc.

Fruit Flours

 * Banana Flour A seldom produced flour made from bananas, Banana flour contains resistant starch and is currently only produced by Mt Uncle in Australia, also the process in which they produce the product is not disclosed.

Flour Products
Some of the many foods made using flour are:
 * bread
 * pasta
 * pastry
 * cake

title: Cookbook:Flour


text:
Cookbook talk:Flour

This module, or a version in the page history, contains text copied from the Wikipedia article Flour, and is used under the GFDL. The page history at the time the text was copied is below:

* (cur) (last). . 16:33, 12 Feb 2004. . Mkweise (Starting bulleted list under ===Types of Flour===) * (cur) (last). . 08:19, 15 Jan 2004. . BRG (links) * (cur) (last). . 12:49, 12 Jan 2004. . Alf Boggis (Added links for millstones and watermills.) * (cur) (last). . 14:19, 11 Jan 2004. . 172.176.146.140 (de:eo:nl:) * (cur) (last). . M 18:48, 18 Nov 2003. . CatherineMunro * (cur) (last). . M 02:02, 16 Nov 2003. . Sdw25 * (cur) (last). . M 02:02, 16 Nov 2003. . Sdw25 * (cur) (last). . 11:16, 24 Oct 2003. . 220.211.156.37 (+ja) * (cur) (last). . 11:34, 20 Aug 2003. . Marshman (add link to seed; add taro flour) * (cur) (last). . 11:30, 20 Aug 2003. . Marshman (add "non-grain") * (cur) (last). . 22:57, 22 Apr 2003. . Jimfbleak (some tweaks) * (cur) (last). . 22:35, 22 Apr 2003. . Kowloonese (explosion) * (cur) (last). . 18:22, 22 Apr 2003. . Jaknouse (several minor things) * (cur) (last). . 18:12, 22 Apr 2003. . Jaknouse (adding lotsa stuff) * (cur) (last). . M 12:07, 21 Jun 2002. . Toby Bartels (Corn to Maize.) * (cur) (last). . 12:19, 11 Jun 2002. . Ark * (cur) (last). . 12:08, 11 Jun 2002. . Ark (improve flow) * (cur) (last). . M 11:43, 11 Jun 2002. . Robert Merkel (stub)

title: Cookbook talk:Flour


text: Template:Meritbadgedisclaimer

title: Template:Meritbadgedisclaimer


text:
Talk:Scouting/BSA/Citizenship in the World Merit Badge

Saudi Arabia map
The map of Saudi Arabia should be from the WikiCommons.

Merit Badge Update
This merit badge was updated this year. The requirements should change to reflect the recent changes.

Requirement 4 is missing the last option, European Union.

Don't Merge This.
Please, don't merge the Family Life MB with this so as not to confuse the two together. LaughingReaper (talk) 01:59, 1 May 2009 (UTC)


text: Talk:Scouting/BSA/First Aid Merit Badge

title: Talk:Scouting/BSA/First Aid Merit Badge


text: Talk:Scouting/BSA/Home Repairs Merit Badge


text: Talk:Scouting/BSA/Mammal Study Merit Badge


text:
Talk:Scouting/BSA/Medicine Merit Badge

Gunpowder does not appear to be relavent to this!

title: Talk:Scouting/BSA/Medicine Merit Badge


text: Template:Sciencemeritbadges

title: Template:Sciencemeritbadges


text: Template:Naturemeritbadges

title: Template:Naturemeritbadges


text: Template:Agriculturemeritbadges

title: Template:Agriculturemeritbadges


text: Template:Businessmeritbadges

title: Template:Businessmeritbadges


text: Template:Nationalinterestmeritbadges

title: Template:Nationalinterestmeritbadges


text: Template:Safetymeritbadges

title: Template:Safetymeritbadges


text: Template:Sportsmeritbadges

title: Template:Sportsmeritbadges


text: Template:Professionsmeritbadges

title: Template:Professionsmeritbadges


text: Template:Hobbiesmeritbadges

title: Template:Hobbiesmeritbadges


text: Template:Developmentmeritbadges

title: Template:Developmentmeritbadges


text:
Cookbook:Onion

Onion in the general sense can be used for any plant in the genus Allium but used without qualifiers usually means Allium cepa, also called the garden onion. Onions (usually but not exclusively the bulbs) are edible with a distinctive strong flavour and pungent odour which is mellowed by cooking. They generally have a papery outer skin over a fleshy, layered inner core. Used worldwide for culinary purposes, they come in a wide variety of forms and colors (but generally brown, white or purple).

The common brown onion tends to have a very pungent odour, and it makes the eyes water. Some varieties have more or less of the eye-watering chemicals, which also makes them taste milder. 'Spanish onions' (the large white onions with a purple skin and purple flecks) are much milder than brown onions, making them more suitable for raw use in salads.

Onions may be grown from seed or very commonly from "sets". Onion sets are produced by sowing seed very thickly one year, resulting in stunted plants which produce very small bulbs. These bulbs are very easy to set out and grow into mature bulbs the following year, but they have the reputation of producing a less durable bulb than onions grown directly from seed and thinned.

Either planting method may be used to produce spring onions or green onions, which are just onions harvested while immature, although "green onion" is also a common name for the welsh onion, Allium fistulosum which never produces dry bulbs and the 'Spring onions' used in Asian cooking are an entirely different variety which never grows a full bulb.

Preparing

Onions may be either served raw or cooked. Cutting onions can be a harrowing experience and often bring tears to the eyes. Folklore says that burning a candle close to the cutting board may decrease the pain. Also, refrigerating onions for an hour or so beforehand will reduce crying and discomfort when cutting.

Onions have a pungent aroma. To remove the smell from hands simply rub hands on the surface of a stainless steel sink and rinse well. White vinegar can also be used to rinse hands, cutting boards, and other utensils to eliminate the onion smell.

Red onions have a milder flavor and may be safely added raw to dishes, most typically salads.

White and brown onions are best cooked. Boiling an onion only creates a bitter flavor, unless steps are taken to reverse the bitterness (boiling in salty water may help). Typically, onions are fried, usually in butter or oil in a skillet or frying pan. The time for which onions are fried before other ingredients are added varies in different cuisines; in Italian, onions are typically fried until translucent, while in Indian recipes, they are fried on a low heat until they are caramelized and turn brown, which produces a different flavour. It's best to fry onions with like vegetables -- garlic, leeks, or scallions. Cooking with acidic vegetables (e.g., tomatoes, tomatillos, or lemons) will disrupt the caramelization process and the onion will never soften. It's best to add acidic vegetables or wine (for deglazing) after the onions are soft.

Related species
The genus Allium is a large one, and most of the species are considered to be "onions" in the looser sense. Commonly raised vegetable alliums include the leeks, garlic, elephant garlic, chives, shallots, welsh onions and garlic chives.

The wild onion (allium ursinum) is collected in the wild, its leaves and bulbs used as food.

Kochbuch/ Zwiebel Livre_de_cuisine/Ingrédients/Oignon Kookboek/Ui

title: Cookbook:Onion


text:
Cookbook talk:Onion

This module, or a version in the page history, uses text taken from the Wikipedia article Plant Families/Onion, and is used under the GFDL. The page history at the time the text was coppied is included below:

 * (cur) (last) . . M 13:32, 24 Feb 2004 . . Robbot (Andre Engels - Robot-assisted disambiguation: Biological cell)
 * (cur) (last) . . 19:27, 23 Feb 2004 . . 218.188.0.150 (+zh:)
 * (cur) (last) . . M 18:45, 23 Feb 2004 . . Elinnea (sv:)
 * (cur) (last) . . M 10:22, 19 Feb 2004 . . Yak (link)
 * (cur) (last) . . M 10:21, 19 Feb 2004 . . Yak (allium ursinum)
 * (cur) (last) . . 11:49, 16 Feb 2004 . . Wouterhagens (added picture)
 * (cur) (last) . . 22:45, 5 Feb 2004 . . WormRunner (onion as allium cepa, links to allium and some related taxa)
 * (cur) (last) . . M 14:15, 5 Feb 2004 . . Hephaestos
 * (cur) (last) . . 14:12, 5 Feb 2004 . . Hephaestos (some rewriting)
 * (cur) (last) . . 21:16, 22 Dec 2003 . . Rfc1394
 * (cur) (last) . . M 06:08, 28 Nov 2003 . . Kowey (ms: (?))
 * (cur) (last) . . 21:35, 2 Nov 2003 . . 218.221.176.3 (+ja)
 * (cur) (last) . . 22:37, 21 Oct 2003 . . 80.12.11.150 (fr:)
 * (cur) (last) . . 13:21, 16 Sep 2003 . . Mihai (wiki)
 * (cur) (last) . . 04:11, 1 Sep 2003 . . 141.53.194.251
 * (cur) (last) . . 04:11, 1 Sep 2003 . . 141.53.194.251 (de)
 * (cur) (last) . . 01:20, 19 Jun 2003 . . Theresa knott (fixed link to cells. This is a stub article please expand)
 * (cur) (last) . . M 22:23, 18 Jun 2003 . . Jimfbleak (sp)
 * (cur) (last) . . M 15:13, 21 May 2003 . . KF
 * (cur) (last) . . 01:59, 20 May 2003 . . Theresa knott (Adding a link to how to prepare an onion cell slide)
 * (cur) (last) . . M 02:31, 10 Oct 2002 . . Olivier
 * (cur) (last) . . M 01:47, 10 Oct 2002 . . 217.168.172.202
 * (cur) (last) . . M 04:49, 3 Oct 2002 . . Andre Engels (nl:)
 * (cur) (last) . . M 16:50, 20 Aug 2002 . . Zadcat (tweak, fix french)
 * (cur) (last) . . 20:17, 21 Jul 2002 . . Perique des Palottes
 * (cur) (last) . . M 19:07, 21 Jul 2002 . . Brion VIBBER (lang link: +eo)
 * (cur) (last) . . M 22:36, 3 May 2002 . . 0

title: Cookbook talk:Onion


text:
Vietnamese/Vietnamization

Yes, Vietnamization has to do with the Vietnam War, but that's not what it means in this case.

With the dawn of television, computers, and the Internet, the use of words that originated with English has increased greatly. This has both increased the importance of English and diminished the importance of other languages. For other languages to keep up, their speakers have to come up with practical translations or transliterations. For Vietnamese, these translations and transliterations are called Vietnamizations. We'll take a look at:

 * how to pronounce English words the way Vietnamese speakers would understand them,
 * how to "Vietnamize" English words, and
 * commonly Vietnamized words

(Much more to come.)

title: Vietnamese/Vietnamization


text:
Cookbook:Pork

| Basic foodstuffs

Pork is the meat from hogs, or domestic swine. The domestication of "pigs" (immature hogs) for food dates back to about 7000 B.C. in the Middle East. However, evidence shows that Stone Age man ate wild boar, the hog's ancestor, and the earliest surviving pork recipe is Chinese, at least 2000-years old. While it is one of the most common meats eaten by the Chinese and Europeans, it is considered inedible under Islamic and Orthodox Jewish law.

Retail Cuts of Fresh Pork
There are four basic (primal) cuts into which pork is separated: shoulder, loin, side and leg.

Shoulder

 * Shoulder Butt, Roast or Steak
 * Blade Steak
 * Boneless Blade Boston Roast
 * Smoked Arm Picnic
 * Smoked Hock
 * Ground Pork for Sausage

Side

 * Spare Ribs
 * Back Ribs
 * Bacon

Loin

 * Boneless Whole Loin (Butterfly Chop)
 * Loin Roast
 * Tenderloin
 * Sirloin Roast
 * Country Style Ribs
 * Chops

Leg

 * Ham/Fresh or Smoked and Cured

Other parts include pigs' feet (what these are called differs between the United States and Great Britain; in the United States only the front feet are used, and the entire front foot [ankle and foot] is called the hock, while in Great Britain both the front and back feet are used, and only the ankle is called the hock, the foot proper being termed the trotters.) Sausage is often made from miscellaneous meats, and scrapple is another aggregate meat-food derived from pigs. Pork intestines are called chitterlings or chitlings. Some pork products, such as pigs' feet, hog jowls, and other parts, not wanted by whites, figured prominently in the traditional diets of southern African-Americans because they were a) available to them and b) affordable for the very poor.

Pork products are often cured by salt (pickling) and smoking. The portion most often given this treatment is the ham; pork shoulder, or front haunch, is also sometimes cured in this manner.

Microorganisms
Pork must be adequately cooked to eliminate disease-causing parasites and bacteria that may be present. Humans may contract trichinosis (caused by the parasite, Trichinella spiralis) by eating undercooked pork. Much progress has been made in reducing trichinosis in grain-fed hogs and human cases have greatly declined since 1950. Today's pork can be enjoyed when cooked to a medium internal temperature of 145 °F (62 °C) or a well-done internal temperature of 170 °F (76 °C).

Some other foodborne micro-organisms that can be found in pork, as well as other meats and poultry, are Escherichia coli, Salmonella, Staphylococcus aureus and Listeria monocytogenes. They are all destroyed by proper handling and thorough cooking to an internal temperature of 145 °F (62 °C).

Hot Fat
Additionally, pork contains fats, which partially liquefy when cooked. These rendered fats are flammable. Water drops coming in contact with hot grease or fat may cause splattering and possible burns. Appropriate fire and personal safety measures should be taken when cooking pork or any other fatty meat.

Other varieties
Bacon, Chorizo, Salami

Pork Recipes
Pork recipes can be found in the recipe index for pork

title: Cookbook:Pork


text:
Cookbook talk:Pork

This module includes text adapted from the public domain US Department of Agriculture article ''[http://www.fsis.usda.gov/OA/pubs/pork.htm SAFETY of FRESH PORK. . . from Farm to Table]''.

This module, or a version in the page history, was copied from the Wikipedia article Pork, and is used under the GFDL. The page history at the time the text was coppied is included below:

 * (cur) (last) . . 14:35, 26 Feb 2004 . . Sfdan (Minor editting)
 * (cur) (last) . . 02:12, 6 Feb 2004 . . 172.130.230.164
 * (cur) (last) . . M 03:59, 4 Feb 2004 . . Pollinator
 * (cur) (last) . . 03:58, 4 Feb 2004 . . Pollinator (copyedit - is this what is meant by "nude"?)
 * (cur) (last) . . 02:50, 4 Feb 2004 . . Meelar (alternate meaning)
 * (cur) (last) . . M 06:06, 29 Jan 2004 . . Meelar (copyedits)
 * (cur) (last) . . 01:39, 19 Jan 2004 . . Error (The taboo. Varieties)
 * (cur) (last) . . 04:30, 12 Jan 2004 . . GRAHAMUK (rm ad-hoc pronunciation, + alternative sp.)
 * (cur) (last) . . M 03:19, 18 Nov 2003 . . Skybunny (Disambiguate 'ham' with Ham (meat))
 * (cur) (last) . . M 13:56, 6 Nov 2003 . . Crusadeonilliteracy
 * (cur) (last) . . 13:51, 6 Nov 2003 . . 218.221.78.67 (+ja)
 * (cur) (last) . . 00:31, 28 Oct 2003 . . Hamton (Hog's jowls!)
 * (cur) (last) . . 10:39, 22 Mar 2003 . . Taw (pl:)
 * (cur) (last) . . 07:42, 4 Nov 2002 . . Kowloonese
 * (cur) (last) . . 12:05, 11 Sep 2002 . . 213.253.40.173 (+o)
 * (cur) (last) . . 12:05, 11 Sep 2002 . . 213.253.40.173 (These traditinal dietary restrictions may have been created to prevent trichinosis, which can be caught from undercooked pork. )
 * (cur) (last) . . 11:58, 11 Sep 2002 . . 213.253.40.173 (trichinosis)
 * (cur) (last) . . M 16:28, 22 Aug 2002 . . Jaknouse (correct link)
 * (cur) (last) . . 16:26, 22 Aug 2002 . . Jaknouse
 * (cur) (last) . . 16:24, 22 Aug 2002 . . Jaknouse (expand a little)
 * (cur) (last) . . 16:22, 15 Jun 2002 . . 195.149.37.106 (*haunch, not curing)
 * (cur) (last) . . 15:58, 15 Jun 2002 . . 195.149.37.106 (*link ham. cured pork, I think.)
 * (cur) (last) . . M 09:32, 15 Jun 2002 . . 64.26.98.90

title: Cookbook talk:Pork


text:
Cookbook:Butter

| Basic foodstuffs | Dairy | Oil and fat

Butter is a fatty dairy product made by churning fresh cream. It is used as a condiment and for cooking in much the same ways as vegetable oils or lard.

Production
Butter is made by agitating cream, which forces the fat droplets to merge together and separate from the liquid portion. This can be done in many different ways and with a variety of tools. Historically, butter churns were used; today, mechanized churning machines make butter in large batches. If the butter is to be colored or flavored, these ingredients are added to the cream before churning; if the butter is to be cultured, a starter culture is added to sour the cream. Once the butter separates from the cream, it is washed to remove residual buttermilk, salted (if applicable), then kneaded and shaped.

To make homemade butter with simple tools, fill a jar ⅓ full with heavy cream. Shake the jar until a solid mass forms. If the cream becomes too thick to shake easily, add a bit of water. Pour off the liquid and use a spatula or spoon to collect the butter. This soft butter can be served on its own, or mixed with herbs or spices. You can also add flavor by pouring a small measure of flavored liquor in with the cream.

Composition
Butter is very high in—but not 100%—fat. North American commercial butter is typically 80–82% fat, while European butter is fattier and richer at about 82–86%. The remaining composition of butter consists of water and milk proteins in emulsion with the fat. The specific fat profile of butter gives it a lower melting point (93°F / 33°C) than other solid fats like shortening—this causes it to melt in the mouth without leaving an unpleasant coating, but this also makes it harder to create very flaky pastries with butter compared to with shortening. Butter is, though, easy to spread at room temperature, which is excellent for its use as a condiment.

Flavor
The flavor of butter depends largely on the diet of the animal that produced the cream, as well as how the cream is processed. Butter made from fresh cream (called sweet cream butter) has a very mild flavor; cultured butter, which is made from soured cream, has a more complex flavor and characteristic buttery taste of diacetyl from the microbial culture. European butter is more likely to be cultured, while North American butter is more likely to be sweet. Butter also comes either salted or unsalted—the exact salt level varies, so salted butter generally should not be used in cooking in order to allow more flexibility and adjustment.

Appearance
Butter is generally pale yellow, but it can vary from deep yellow to nearly white depending largely on what type of food the animals were eating. For example, butter is typically paler in the winter, when dairy cattle feed on stored hay rather than fresh grass. Annatto may be added to pale butter in order to give it a more golden hue.

Commercially available butter tends to be packaged in blocks; butter in the USA is commonly sold by the pound, divided into four "sticks". It can also be whipped or aerated to lighten it—this should not be used in cooking if measuring by volume.

Selection and storage
Butter is very stable and has a long shelf-life, but it will still go bad after a long period. Because the fat can eventually oxidize and turn rancid in contact with air, butter should be kept wrapped or covered. It can also go sour from bacterial contamination—you will generally be able to tell whether butter has gone bad from its flavor and aroma. It will keep well for months when wrapped and stored in the fridge or freezer. Clarified butter, which has all the water removed, will typically last even longer.

Use
Butter is widely used in cooking and baking for its flavor and texture. It can be used to fry foods, but it is not ideal for high-heat cooking, since the milk proteins it contains give it a low smoke point of about 260°F (127°C). If the flavor of butter is desired for high-heat cooking, it is best to use clarified butter, whose milk proteins have been removed. Butter is also often used as a simple condiment, and it may be spread on bread products or stirred into dishes like pasta before eating. Butter can also be used to thicken and flavor sauces and custards, such as when "mounting" a sauce by emulsifying in small pieces of the fat.

In baking, butter adds tenderness and moisture to baked goods, and the temperature and texture of the butter is often carefully controlled to affect the final texture of the product. If making a flaky or laminated pastry, it is best to use higher-fat European-style butter, which is slightly more workable and less likely to melt into the dough.

Various techniques exist to add additional flavor to butter. For example, browned butter or beurre noisette is made by gently cooking butter until its milk proteins brown, giving the final product a nutty flavor. Compound butters are simply made by incorporating flavorful ingredients such as herbs, anchovies, and sweeteners into soft butter before using or serving.

title: Cookbook:Butter


text:
Cookbook:Egg

Bird and fish eggs are common food sources. This chapter discusses bird eggs only—for fish eggs, see roe.

Composition
For the purposes of cooking, chicken and other bird eggs consist of the following major parts; all but the shell are edible:

 * Shell: hard outer covering consisting largely of calcium carbonate
 * Membrane: thin, flexible layer between the shell and the white
 * White: clear, viscous fluid consisting primarily of albumen protein and water
 * Yolk: yellow center, consisting of fats and proteins
 * Chalaza: fibrous white cord connecting the yolk to the shell

Shell
The shell is the hard outer layer of a poultry egg, made primarily of calcium carbonate. Its primary function is to keep the egg safe, preventing foreign material and contaminants from getting inside. It does, however, contain minuscule pores that allow gases and other tiny molecules to permeate. The most common colors are white and brown, though specialty chicken eggs may be blue or have speckles. The color of the eggshell has no bearing on nutritional content or other properties of the egg.

White
After the shell, the next major component of the egg is the white, also called albumen, which consists primarily of water and protein. Unlike the egg yolk, it contains little fat. The white makes up about 67% of the de-shelled chicken egg, and it is further subdivided into the thin white and the thick white, as well as the chalazae. The thin white is thinner and more watery, while the thick white surrounds the yolk and is firmer. The chalazae are harmless strands that hold the yolk in place and degrade with age.

Of the many proteins in the white, ovalbumin is the main constituent. The major proteins found in egg white (> 1% of the total protein content) are listed below:

 * Ovalbumin 54%
 * Conalbumin 13%
 * Ovomucoid 11%
 * Lysozyme 3.5%
 * Globulins (G2, G3) 8.0% (?)
 * Ovomucin 1.5%

Yolk
In the center of the egg white is the round, yellow yolk, which is about 33% of the de-shelled chicken egg. Like the white, it has a substantial protein content (~15–16%). However, unlike the white, it contains a significant proportion of fats (~32–35%). The intensity of the yolk color and flavor depend primarily on the diet of the laying bird —foods like marigold, alfalfa, and yellow corn contain more yellow-orange pigments and will therefore give a more intense color to the yolk. This color is generally not reflective of egg quality, though some may prefer a more intense coloration. The yolk may sometimes have a spot of blood on it—this is harmless.

One important constituent of the yolk is lecithin, an emulsifier that helps blend together fats and water —this emulsifying quality contributes to eggs some of their most useful properties. Heating egg yolk for an extended period can cause it to develop a greenish-grey color as a result of the reaction between iron in the yolk and sulfur in the white. This is harmless but sometimes unappealing. Sulfur also contributes a distinctly "eggy" flavor, which gets stronger with egg age and heating.

Coagulation
All proteins, including those in egg white, are made of long chains of amino acids which. In a raw egg, these strings are raveled up in a tangled compact mass. As an egg is heated, the heat causes the bonds within the proteins to break, a process called denaturation. As these proteins strings unfold and entangle with other proteins, new bonds form between them, causing the coagulation and set texture in a cooked egg. Overheating the egg for too long a period causes the protein network to overly contract, which ends up squeezing out moisture instead of trapping it—thus, overcooked eggs are dry and rubbery. Additionally, it's important to note that when heated too quickly, the egg proteins don't properly unravel, so they make a weaker thickener. Gentle and slow heating thereby improves the thickening capacity of the egg.

Because of their different components, the egg white and yolk set at different temperatures. The following table shows the temperatures at which different egg components denature and coagulate: By combining the eggs with other ingredients, it becomes possible to modulate the temperature of coagulation. Simple dilution raises the required temperature by physically separating the egg proteins. Sugar, starch, and fat also interfere with the proteins' ability to unravel and reconnect, so adding these also raises the coagulation temperature. Conversely, adding acid to the mixture tends to speed up the protein denaturation, which lowers the temperature of coagulation.

The texture of cooked egg can also be modulated by physical disturbance. Regular stirring of an egg mixture while heating breaks up the mixture somewhat, which prevents it from solidifying into one large mass. This is why stirring a custard or an omelet gives it a softer texture than letting it cook undisturbed.

Aging
As a whole egg ages in its shell, a number of changes take place, most of which are caused by the pores in the shell. First, over time, carbon dioxide dissolved in the egg diffuses out through the shell; this has the effect of making the egg more alkaline over time, and the egg becomes thinner and flatter. In addition to carbon dioxide, moisture also escapes through the pores as the egg ages, and the incoming air expands the air pocket inside the egg. Thus, older eggs will increasingly float in water.

Species
All birds lay eggs, and several domesticated birds regularly lay unfertilized eggs, which we use as food. For example, duck, goose, quail, turkey, and ostrich eggs (the largest edible bird eggs in the world) are all eaten, each with their own particular characteristics. However, the most commonly used egg by far is the chicken egg, and the term "egg" without any other qualifiers will refer to chicken eggs in this Cookbook and elsewhere.

Processing
While whole, fresh eggs are the standard, a variety of processed "egg products" are available for purchase. In-shell heat-treated eggs are available to reduce the risk from eating undercooked eggs, though these are not suitable for foaming. Raw eggs can also be pre-shelled and sold as liquid or frozen eggs, yolks, or whites. They can also be dried and powdered, after which stabilizers may be added to help them whip better.

Sizing
Many countries have a standardized sizing system for chicken eggs, though the terminology used by each system is different and may not agree with the others. So, for normal recipes, it is best to avoid specifying egg size. In general, most recipes use "standard" eggs unless otherwise specified, which correspond to USDA size large and EU size M; these standard eggs tend to weigh about 50–60 g each out of shell.

EU weight standard
EU eggs are specified as per-egg weight ranges, plus a per-100 minimum.

USDA weight standard
USDA eggs are specified as the minimum weight of a dozen.

Selection and storage
Eggs are most often procured whole, in their shells. When purchasing, inspect the eggs for any cracks in the shells. Do not purchase or use any cracked eggs, as they are easily contaminated.

Keeping
Eggs can "go bad" in two primary ways. The first is spoilage caused by microbial contamination, which results in a bad odor and can cause food poisoning. You can easily detect this kind of spoilage by smell. The second way is a side effect of simple aging, where the egg simply degrades in quality and dries out —this does not necessarily pose any danger, but it is reflective of lower quality. A simple method for testing if eggs have gone bad involves submerging them in a deep container of water, such as a glass or large bowl. Eggs that touch the bottom of the container are usually good, while eggs that float entirely are no longer good to eat.

Refrigeration
Whole eggs may be stored at room temperature or in the fridge, depending on how they are processed. Chicken eggs are covered in a protective layer called the cuticle, which helps prevent bacterial contamination and subsequent spoilage. Eggs in the European Union and many other places leave this layer intact, and these eggs can be safely stored at cool room temperatures for up to a few weeks. However, some regions such as the United States have most commercially-available eggs undergo a washing process that removes external contaminants but strips the protective cuticle from the egg; this slightly increases the risk of microbial contamination from minuscule cracks, thereby necessitating storage in the refrigerator to prevent spoilage. It has, however, been noted that refrigeration does extend the shelf life of eggs, regardless of whether or not they have been washed. Whole eggs kept in the back of the fridge (not the door, where it is warmer) will remain good for many weeks. Cracked eggs will last for up to a few days.

Freezing
Egg whites can be easily frozen as is, though they will not foam as well after thawing. Yolks, however, thicken irreversibly if frozen without treatment. To reduce this risk, mix the yolks with ⅛ tsp salt or 1½ tsp corn syrup per 4 standard yolks. Thaw frozen eggs in the fridge or cool water.

Food-borne illness
Though relatively rare, raw eggs may be contaminated with Salmonella bacteria, which can cause food poisoning. They should therefore be avoided by those with weak or undeveloped immune systems, such as the elderly, infirm, or pregnant. Note that while proper storage reduces the risk of eggs going bad, it does not eliminate the risk of salmonella poisoning. Unwashed eggs may pick up salmonella on the outside of the shell, which can then contaminate foods, while in rare cases salmonella may enter the egg before it is laid. The bacteria can only be killed by heating (5 minutes at 140°F/60°C or 1 minute at 190°F/88°C).

Explosion
Due to the formation of steam inside the shell, whole eggs can explode if cooked above boiling temperatures. Never microwave or bake a whole egg.

Separating eggs
Separating eggs is when the yolk and the white are physically separated from each other. One traditional way to separate an egg is to crack the egg into two roughly equal parts, and pass the yolk from one half of the shell to the other, letting the white fall into a bowl below; however, this runs the risk of breaking the yolk with the shell and contaminating the white with it. A simpler way is to crack the egg into your clean hand and let the white run through your fingers. Similarly, you can crack the entire egg into a bowl and gently scoop the yolk out with your hands. Generally, it is easier to separate eggs when cold, since the yolks are slightly firmer and will puncture less easily.

Foaming
Eggs are excellent foaming agents, as the egg proteins unravel and form a stable network around the air bubbles when whipped. The protein is elastic, so when the egg white is cooked, and the air expands, the white stretches and sets in the expanded position. Egg whites in particular can be whipped to a much greater degree (8 times their liquid volume), since the fat present in the yolks disrupts the protein network stabilizing the bubbles. Even a tiny amount of residual fat from other sources will inhibit the foaming of egg whites.

A few things will improve the stability of egg white foams. The first is to use fresh egg whites, which will foam slower but more stably than older whites. The second is to add a little cream of tartar or another acid, which helps the proteins denature and stick together to form a more stable foam. Sugar also stabilizes the foam, which is why a meringue is more stable than a simple whipped white mixture. Finally, whipping the whites in a copper bowl creates a more stable foam that is more resistant to overbeating. Note that cream of tartar should not be used if a copper bowl is used, because it can react with the copper and force more of it into solution, thus potentially increasing the toxic effect.

Note that when using egg whites as a leavening agent in batters, it is better to whip them to medium rather than stiff peaks. This is because stiff peaks will be harder to incorporate into the batter and risk deflating during the process, and because stiff whites can over-expand and collapse when heated in the oven.

Tempering
Eggs must always be tempered when incorporating them into hot liquids. Otherwise, you risk curdling the eggs before they can be properly incorporated.

Peeling
The membrane and shell of fresh chicken eggs cling to the egg white when it is hard-boiled, making it nearly impossible to de-shell/peel—older eggs are better for this purpose. Alternatively, shock the eggs in cold water for a few minutes after you're done boiling them.

Use
There are numerous ways to prepare eggs as the focus of a dish, such as baking, boiling, frying (straight or scrambled), and poaching.

Eggs are also widely incorporated into dishes, both sweet and savory, where they play a variety of roles. Owing to the coagulation ability of their constituent proteins, eggs frequently contribute binding capacity, structure, and stability to cooked preparations. This is particularly notable in goods like cakes and custards. The fat and water content in eggs help prevent starch retrogradation and slow staling in baked goods. Egg yolks help emulsify various sauces, and egg whites are used to help remove sediments from liquids like wine and stock in order to clarify them. Through their foaming capacity, eggs are often an important leavening or lightening agent. Examples include mousses, soufflés, and cakes. Eggs also contribute richness of flavor and golden color to foods, and egg washes are often applied to baked goods to enhance their appearance.

When incorporating eggs into mixtures, it is easiest to use room temperature eggs. In particular, you must not incorporate cold eggs into a mixture with a solid fat, since the cold can cause the fat to curdle and not properly incorporate. Letting cold eggs sit in warm water is a great way to quickly warm them up for use.

Avoid using aluminum tools when working with eggs, since they will discolor the eggs and impart a grey color.

Substitution
In some cases, eggs from different birds can be substituted for chicken eggs. If doing so, you'll want to adjust the number of the non-chicken eggs to get the same weight equivalent of chicken egg. However, it is important to note that non-chicken eggs can have a different ratio of yolk to white, which will impact texture, and they may have a slightly different flavor as well. Generally speaking, it's safe to use non-chicken eggs in stovetop recipes that focus primarily on the egg, like omelets.

For those who do not eat yolks, replacing the yolk with extra egg white in whole-egg recipes can work. Many whole-egg substitutes like Egg Beaters are based on egg whites. Do note that leaving out the yolks will remove some flavoring and emulsification power, and the mixture will set and dry a little earlier.

For those who do not eat any eggs at all, there are a few substitution options depending on the dish. No egg substitutes are perfect replacements, and most are very application-specific, but in many recipes an acceptable finished product can be achieved. Tofu plus seasonings are often used as a substitute for scrambled eggs. Cornstarch (1 tbsp dissolved in 3 tbsp warm water per egg) or soy flour (1 tbsp + 2 tbsp water) can be used when egg is required for thickening. For baking, ground flax or chia seeds (8 g/1 Tbsp gelled in 45 ml/3 tbsp water) can be used in doughs and batters that are dark enough for the seeds to be unnoticeable. For light-colored doughs and batters, 45 ml/3 Tbsp aquafaba or 1 tbsp cornstarch in 3 tbsp warm water is recommended. Other options for sweet or fruity doughs and batters include one mashed ripe banana or 60 ml/¼ cup applesauce per egg. If you want the foaming properties of egg whites, aquafaba is a reasonable substitute. Adding ¼ teaspoon cream of tartar per 4 egg equivalents will help the aquafaba whip stiff.

title: Cookbook:Egg


text:
Applicable Mathematics

Contents

 * 1) /Systems of Equations/
 * 2) /Matrices/
 * 3) /Univariate Data/
 * 4) /Sets/
 * 5) /Transformations/
 * 6) /Probability/
 * 7) /Counting Techniques/
 * 8) /Bivariate Data/
 * 9) /Linear Programming and Graphical Solutions/
 * 10) /Probability Distributions/
 * 11) /Odds/

title: Applicable Mathematics


text:
Template:ApplicTOC

Home - 1 - 2 - 3 - 4 - 5 - 6- 7 - 8 - 9 - 10

TOC

title: Template:ApplicTOC


text:
Cookbook talk:Nuts and Seeds

The text for this module, or a verson of this module in the page history, was copied from the Wikipedia article Nut. The page history at the time the text was coppied is below:

 * (cur) (last) . . 07:21, 18 Dec 2003 . . 199.46.198.230
 * (cur) (last) . . 07:20, 18 Dec 2003 . . 199.46.198.230
 * (cur) (last) . . 19:16, 26 Nov 2003 . . Marshman (Fix link > pinon)
 * (cur) (last) . . M 04:16, 17 Oct 2003 . . Heron (sp)
 * (cur) (last) . . M 03:28, 29 Sep 2003 . . Modemac
 * (cur) (last) . . 08:07, 28 Sep 2003 . . 138.23.202.157 ([M] Link formatting; remove header that isn't followed.)
 * (cur) (last) . . 14:39, 4 Sep 2003 . . Marshman (Add link >> Cuisine)
 * (cur) (last) . . 14:29, 4 Sep 2003 . . Marshman (Link to Botany; remove questional statement about nuts in a forest)
 * (cur) (last) . . 10:43, 3 Sep 2003 . . Marshman (Fix links; copy edit text)
 * (cur) (last) . . 16:51, 2 Sep 2003 . . Marshman (Correct terminology and remove bad examples, add good examples)
 * (cur) (last) . . M 15:40, 26 Aug 2003 . . Marshman (Fix link >>Fabaceae)
 * (cur) (last) . . 03:38, 23 Aug 2003 . . 169.207.90.200
 * (cur) (last) . . M 04:25, 6 Aug 2003 . . Heron (wiki link)
 * (cur) (last) . . 13:47, 27 Jun 2003 . . Heron (coco de mer is even bigger than coconut)
 * (cur) (last) . . 07:06, 23 Jun 2003 . . 207.215.68.169 (moved old content about food nuts from Nut plus a re-write)

title: Cookbook talk:Nuts and Seeds


text:
Statistics

Welcome to the Wikibook of Statistics

Statistics - Area of applied mathematics concerned with the data collection, analysis, interpretation and presentation.

Statistics is used in almost every field of research: the discovery of the Higgs particle, social sciences, climate research,... With this, and with its well established foundations, it is very well suited for a wikibook. This book is an ongoing effort to make this basic knowledge available for free.

Since the concepts in probability are essential for statistics, a thorough knowledge of probability is needed before reading this book (especially for the advanced part), and so probability is a prerequisite of this book. Although some concepts in the probability are reviewed, the review is meant to be read by someone who is familiar with those concepts already, and so it is not too detailed. For a more detailed discussion on those concepts, you may refer to the wikibook Probability.

This book is divided into two main parts: Basics and Advanced. The Basics part gives a brief introduction and idea about statistics, while the Advanced part gives a more formal and mathematical treatment on statistics. =Contents= Basics
 * Introduction
 * Datatypes
 * Methods of Data Collection
 * Data Analysis
 * Summary Statistics
 * Data Display
 * Probability (see Probability wikibook for more details)
 * Distributions (see Probability wikibook for more details)
 * Hypothesis Tests

Advanced
 * /Preliminaries/
 * /Point Estimation/
 * /Interval Estimation/
 * /Hypothesis Testing/
 * Numerical Methods
 * Multivariate Data Analysis

Examples
 * Practice Problems
 * Analysis of Specific Datasets

Appendix
 * Authors
 * /Glossary/
 * /Index/
 * /Links/
 * Statistics/Summary, Study Guide and Formulas

title: Statistics


text:
Cookbook:Cuisine of the United Kingdom

| European cuisines

The cuisine of the United Kingdom (UK) is highly influenced by Britain's location as an island nation off of the coast of mainland Europe, with its close proximity to the polar jetstream causing famously unpredictable weather alongside distinct seasonal changes that lends to food distinctly associated to different parts of the year as crops go in and out of season. This seasonality is further seen in the UK's access to the sea, with seafood changing throughout the year and differing dishes across the year's calendar changing from one month to the next.

Alongside its geography, the history of the British Isles and the history of the UK's development throughout the decades has played an extremely important part in defining its cuisine heritage. The legacy of Roman occupation, Viking invasions, and French conquests have all left their mark on the food of this island. The unique political and cultural ties across the nations of England, Wales, Scotland, and Ireland have also influenced its cuisine as their cultures have merged and clashed. The British Empire, once the world's largest empire, also had substantial influence to British cuisine as the expansion and occupation of lands across the world introduced new recipes, ingredients, and ways of thinking about food. The aftermath of World War One and World War Two, from food rationing to losses in trade, additionally influenced cooking and cuisine in the UK as recipes were adapted to fit austere times.

From here, the post-modern period and rapid globalisation of our world has created new opportunities and challenges to British cuisine. From near 24 hour access to supermarkets, globally sourced ingredients, and easily accessible recipes (like the ones found here!) create a whole new world for British cuisine to thrive within. However, British cuisine also faces issues from food inequality, climate change impacts, and obesity that are ongoing threats to the safeguarding of food security, quality, and enjoyment of everyone.

British cuisine reflects and incorporates something from all the cultures and countries Britain has had contact with throughout its long history. Indeed British cooking has inspired many culinary traditions around the world. We hope this cookbook reflects the rich tradition of British cooking in its broadest sense.

Savoury Dishes

 * Bangers & Mash

 * Bubble and Squeak
 * Champ
 * Chip Butty
 * Corned beef hash
 * Corned beef pie
 * Cornish Pasty and Pastry for Cornish Pasties
 * Coronation Chicken
 * English Breakfast
 * Friar's Omelette
 * Fish and Chips
 * Haggis
 * Kedgeree
 * Lancashire Hotpot
 * Liver and onions
 * Mushy Peas
 * Pastie
 * Pease pudding
 * Ploughman's Lunch
 * Roast Beef
 * Sausagemeat Pie
 * Scouse or Lobscouse
 * Shepherd's Pie
 * Stargazy Pie
 * Steak and Ale Pie
 * Steak and Kidney Pudding
 * Toad In The Hole
 * Ulster fry
 * Welsh Rarebit
 * Yorkshire Pudding

 * Some UK savoury dishes not included yet:
 * Cauliflower cheese
 * Cottage pie
 * Faggot
 * Sausage roll
 * Scotch egg

Desserts

 * Banoffee Pie
 * Christmas Pudding
 * Custard

 * Eton Mess
 * Figgy Hobbin
 * Jam Roly-Poly
 * Lemon Meringue Pie
 * Mincemeat Tart/Mince pie
 * Potato Pudding
 * Queen of Puddings
 * Rhubarb Crumble
 * Sticky Toffee Pudding
 * Summer Pudding
 * Trifle

 * Some UK pudddings not included yet:
 * Bakewell tart
 * Spotted dick
 * Eccles cake

Cakes and Sweets
These should be accompanied with a nice cup of tea:

 * Basic Flapjacks
 * Caramel Squares (aka Millionaire Shortbread)
 * Christmas cake
 * Cornish Fairings
 * Deep Fried Mars Bar
 * Fairy Cakes (and Butterfly Cakes)
 * Gingerbread (and Parkin)
 * Pound Cake
 * Scones
 * Shortbread
 * Victoria Sandwich (aka Victoria Sponge)

 * Some UK cakes not included yet:
 * Chorley cakes
 * Eccles cakes
 * Iced buns

Drinks
English breakfast tea

title: Cookbook:Cuisine of the United Kingdom


text:
Macroeconomics/Multiplier Process

=Multiplier! (k)=

{| WIDTH="100%"
 * style="background-color: #FFFFEE; border: solid 1px #FFC92E; padding: 1em;" valign="top" |
 * style="background-color: #FFFFEE; border: solid 1px #FFC92E; padding: 1em;" valign="top" |

The simple multiplier
The number of times total income increases corresponding to an increase in the investment is known as investment multiplier

Assumptions:

 * Two sector economy
 * Induced consumption and savings only
 * Constant prices
 * Some unemployed resources in the economy
 * }

Formula

 * The simple investment can also be expressed by:

 * For example if Y (national Y) rises by $5000 as a result of an increase in investment of $1000 then the k coefficient is 5 (5000/1000).

Note:

 * 1) The larger the MPC the larger the multiplier
 * 2) The multiplier process also operates in reverse.

Derivation
Assume the MPC of a hypothetical economy is 0.5. If a person spends $1 on a widget, then the person who sells it receives $1 of income, of which a portion is spent (MPC), this person then uses their $0.5 to purchase another good ad infinitum. Expressing this mathematically:
 * $$1+MPC+MPC^2 + \cdots $$
 * As $$MPC \leq 1 $$ then what results is the limiting sum of a geometric sequence.
 * i.e. $$S_{ \infty}=1+MPC+MPC^2 + \cdots = {1 \over 1 - MPC} $$ (letting a=1, r=MPC)
 * letting $$S_{ \infty}=k \Rightarrow k = {1 \over 1 - MPC} $$
 * As $$MPS + MPC = 1 $$ then,
 * $$ k = {1 \over 1 - MPC} = {1 \over MPS} $$

Table:

 * The multiplier shows how one man's spending creates another man's income, through several time periods. In this case an initial new investment of $10 creates new income of $10, which is either spent or saved by those who have earned it. The proportion which is spent creates income for others in the second time period (shown by arrows from one period to the next). This is also spent or saved. The final new income which has flowed from the initial investment can be determined using the formula [$$Y = k \times initial\ investment$$] (i.e. $$ 5 \times 10 = 50$$). Had the MPC been higher (say 0.9) the multiplier would be larger and more income would have been created.

Graph:

 * .This diagram assumes no government and no trade, so AE = C + I.
 * Initial equilibrium occurred at the red dot on the upper panel of the diagram, where $300 was earned and spent by households and firms. S = I at $60 (red dot on the lower panel).
 * Then firms decided to increase I by $10 (shown on the diagram as I + ΔI). This created extra income in the economy, which gave consumers extra spending power. Because one man's spending is another man's income, there was a series of C, S and Y increases similar to those at the green dot on the upper panel of the diagram, where planned levels of expenditure and income had risen to $350. Once again, S = I at $70. The new equilibrium occurs at a higher level of income. A small change in investment has resulted in a large change in AY.

title: Macroeconomics/Multiplier Process


text:
Macroeconomics/Expanded Multipliers

=Expanded Multipliers=
 * The simple k assumes no government or overseas (o/s) sectors in the economy. In reality Y will be subject to taxation, imports and savings before it will be spent in the domestic economy. Thus various complex multipliers incorporates these flows and is a smaller coefficient than [k = 1/MPS].

The Multiplier

 * The operation of the multiplier is essentially the same but consumption is reduced by acknowledging the other leakages in the economy.
 * This multiplier is applicable to all direct spending in the economy, including government spending.

Taxes/Transfers Multiplier

 * This multiplier is applicable to all indirect injections into the economy, such as cutting taxes or increasing government transfers. The multiplier is positive because it implies a positive change, or increase, in the input. (taxes).

Balanced Budget Multiplier

 * This multiplier is used when the government increases spending and uses a tax increase to pay for the spending. To model change in expenditure when the government decreases spending and cuts taxes to cover the costs, multiply by a negative input in expenditure.

title: Macroeconomics/Expanded Multipliers


text:
Waves/Waves in two and three Dimensions

Waves in Two and Three Dimensions
In this chapter we extend the ideas of the previous chapter to the case of waves in more than one dimension. The extension of the sine wave to higher dimensions is the plane wave. Wave packets in two and three dimensions arise when plane waves moving in different directions are superimposed.

Diffraction results from the disruption of a wave which is impingent upon an object. Those parts of the wave front hitting the object are scattered, modified, or destroyed. The resulting diffraction pattern comes from the subsequent interference of the various pieces of the modified wave. A knowledge of diffraction is necessary to understand the behavior and limitations of optical instruments such as telescopes.

Diffraction and interference in two and three dimensions can be manipulated to produces useful devices such as the diffraction grating.

title: Waves/Waves in two and three Dimensions


text:
Arabic/Arabic alphabet (by group)

Recognising Characters
Written Arabic has 4 forms for each letter. This might appear much at first, but it's not as hard as you might think. For starters, Arabic does not have any capital letters, so this drops us from 4:1 ratio with the Roman alphabet to a meager 2:1 ratio. Secondly, Arabic does not have a separate cursive and manuscript versions of the letters; since what you're learning already is cursive, one could conceivably argue that we're dropping from a 2:1 to a 1:1 ratio.

There's better news still. A lot of these letters are really just derivations of other letters, and many of the ones that aren't derivations behave in a similar enough fashion to be learned together. This page is aimed at exploiting these similarities to help you learn how to read and write Arabic letters.

At a glance
Here are the letter-groups at a glance. We mentioned earlier that there are 4 forms for each character: isolated, initial, medial and final. In this table, we only show the isolated form of each character. But we also break the letters into groups that have similar shapes. Notice how some letters are derived from other letters by adding dots above or below some base form. You might be wondering why it is claimed that certain letters are similar to each other. (FIXME: for example). This is because the table is organised by similarity the medial form of each letter, that is the shape the letter takes when it is in the middle of a word. Let's proceed to the next set of tables, where you shall learn about these forms in greater detail.

''Disclaimer: the organisation of letters into groups is based strictly on the authors' personal opinions. If an authority on the Arabic language tells you that things are otherwise, you should believe them and not us''

Arabic letters in detail
Now, we will look at each of the letter classes in detail. Every row in this table represents a separate letter. There are 8 constant letters, 6 isolated ones, 5 curve-pointy ones, 5 hook ones, and 4 other ones. You'll note also that we group the rows by number of dots; this is to show you the similarities between letters that differ only by the dots that they use. Even though ba ( ب ) and tha ( ث ) are completely different letters, they pretty much act the same way.

Constant
The constant forms behave roughly the same way no matter what position they are in.

Note: technically fa and qa are not related to each other, but for us, being beginners, we'll pretend that they are for now.

Isolated
The isolated characters do not connect to the next letter in the medial form. Consider alef and lam... written in the middle of words, they would look almost the same, but because alef does not connect to the next character (ـاـ) but lam does (ـلـ), you can tell them apart.

Curve-pointy
The curve-pointy letters have a single curve in isolated or initial form, but when they are in the middle of a word, they form a simple point up.

Hook
The hook letters have a downward hook in their final form and an upward hook in their medial form.

Other
Finally, there are four letters which have their own idiosyncratic behaviours.

Tâ marbûta
One letter which you will encounter rather frequently is the tâ marbûta (ة, not to be confused with ه). This letter always occurs in final position and has two forms:

Ligatures
Sometimes two letters combine (and form a ligature) to be written in a prettier or more convenient manner. When lam ( ل ) is followed by alif ( ا ), it generally forms the lam-alif ligature ( لا ):

title: Arabic/Arabic alphabet (by group)


text:
Template:Waves/2-3DWavesTOC

Waves : 2 and 3 Dimension Waves 1 - 2 - 3 - 4 - 5 - 6 - 7 Problems
 * This template is part of the Waves book. This serves as a partial TOC for all pages in the section "2 and 3 Dimensional Waves". This template should appear at the top and bottom of every page in that section.

title: Template:Waves/2-3DWavesTOC


text:
Waves/Plane Waves

Plane Waves
A plane wave in two or three dimensions is like a sine wave in one dimension except that crests and troughs aren't points, but form lines (2-D) or planes (3-D) perpendicular to the direction of wave propagation. Figure 2.5 shows a plane sine wave in two dimensions. The large arrow is a vector called the wave vector, which defines (1) the direction of wave propagation by its orientation perpendicular to the wave fronts, and (2) the wavenumber by its length. We can think of a wave front as a line along the crest of the wave. The equation for the displacement associated with a plane sine wave in three dimensions at some instant in time is
 * $$ A(x,y,z) = \sin (\mbox{k} \cdot \mbox{r} ) = \sin (k_x x + k_y y + k_z z) . $$ (3.9)

Figure 2.5: Definition sketch for a plane sine wave in two dimensions. The wave fronts are constant phase surfaces separated by one wavelength. The wave vector is normal to the wave fronts and its length is the wavenumber. Since wave fronts are lines or surfaces of constant phase, the equation defining a wave front is simply $$\mbox{k} \cdot \mbox{r} = const$$.

In the two dimensional case we simply set $$k_z = 0$$. Therefore, a wavefront, or line of constant phase $$\phi $$ in two dimensions is defined by the equation
 * $$ \mbox{k} \cdot \mbox{r} = k_x x + k_y y = \phi \quad \mbox{(two dimensions)} . $$ (3.10)

This can be easily solved for $$y$$ to obtain the slope and intercept of the wavefront in two dimensions.

As for one dimensional waves, the time evolution of the wave is obtained by adding a term $$- \omega t$$ to the phase of the wave. In three dimensions the wave displacement as a function of both space and time is given by
 * $$ A(x,y,z,t) = \sin (k_x x + k_y y + k_z z - \omega t ) . $$ (3.11)

The frequency depends in general on all three components of the wave vector. The form of this function, $$\omega = \omega (k_x, k_y , k_z )$$, which as in the one dimensional case is called the dispersion relation, contains information about the physical behavior of the wave.

Some examples of dispersion relations for waves in two dimensions are as follows:

 * Light waves in a vacuum in two dimensions obey
 * $$ \omega = c ( k_x^2 + k_y^2 )^{1/2} \quad \mbox{(light)}, $$ (3.12)
 * where $$c$$ is the speed of light in a vacuum.

 * Deep water ocean waves in two dimensions obey
 * $$ \omega = g^{1/2} ( k_x^2 + k_y^2 )^{1/4} \quad \mbox{(ocean waves)}, $$ (3.13)
 * where $$g$$ is the strength of the Earth's gravitational field as before.

 * Certain kinds of atmospheric waves confined to a vertical $$x-z$$ plane called gravity waves (not to be confused with the gravitational waves of general relativity)3.1 obey
 * $$ \omega = \frac{N k_x}{k_z} \quad \mbox{(gravity waves)}, $$ (3.14)
 * where $$N$$ is a constant with the dimensions of inverse time called the Brunt-Väisälä frequency.

Figure 2.6: Contour plots of the dispersion relations for three kinds of waves in two dimensions. In the upper panels the curves show lines or contours along which the frequency $$\omega $$ takes on constant values. For light and ocean waves the frequency depends only on the magnitude of the wave vector, whereas for gravity waves it depends only on the wave vector's direction, as defined by the angle $$\theta $$ in the upper right panel. These dependences for each wave type are illustrated in the lower panels.

Contour plots of these dispersion relations are plotted in the upper panels of figure 2.6. These plots are to be interpreted like topographic maps, where the lines represent contours of constant elevation. In the case of figure 2.6, constant values of frequency are represented instead. For simplicity, the actual values of frequency are not labeled on the contour plots, but are represented in the graphs in the lower panels. This is possible because frequency depends only on wave vector magnitude $$(k_x^2 + k_y^2 )^{1/2}$$ for the first two examples, and only on wave vector direction $$\theta $$ for the third.

title: Waves/Plane Waves


text:
Waves/Plane Superposition

Superposition of Plane Waves
We now study of wave packets in two dimensions by asking what the superposition of two plane sine waves looks like. If the two waves have different wavenumbers, but their wave vectors point in the same direction, the results are identical to those presented in the previous chapter, except that the wave packets are indefinitely elongated without change in form in the direction perpendicular to the wave vector. The wave packets produced in this case march along in the direction of the wave vectors and thus appear to a stationary observer like a series of passing pulses with broad lateral extent.

Superimposing two plane waves which have the same frequency results in a stationary wave packet through which the individual wave fronts pass. This wave packet is also elongated indefinitely in some direction, but the direction of elongation depends on the dispersion relation for the waves being considered. One can think of such wave packets as steady beams, which guide the individual phase waves in some direction, but don't themselves change with time. By superimposing multiple plane waves, all with the same frequency, one can actually produce a single stationary beam, just as one can produce an isolated pulse by superimposing multiple waves with wave vectors pointing in the same direction.

Two Waves of Identical Wavelength
If the frequency of a wave depends on the magnitude of the wave vector, but not on its direction, the wave's dispersion relation is called isotropic. In the isotropic case two waves have the same frequency only if the lengths of their wave vectors, and hence their wavelengths, are the same. The first two examples in figure 2.6 satisfy this condition. In this section we investigate the beams produced by superimposed isotropic waves.

We superimpose two plane waves with wave vectors $$\mbox{k}_1 = (- \Delta k_x, k_y )$$ and $$\mbox{k}_2 = ( \Delta k_x , k_y )$$. The lengths of the wave vectors in both cases are $$k_1 = k_2 = ( \Delta k_x^2 + k_y^2 )^{1/2}$$:
 * $$ A = \sin ( -\Delta k_x x + k_y y - \omega t ) + \sin (\Delta k_x x + k_y y - \omega t ) . $$ (3.15)

If $$\Delta k_x << k_y$$, then both waves are moving approximately in the $$y$$ direction. An example of such waves would be two light waves with the same frequencies moving in slightly different directions.

Figure 2.7: Wave fronts and wave vectors of two plane waves with the same wavelength but oriented in different directions. The vertical bands show regions of constructive interference where wave fronts coincide. The vertical regions in between the bars have destructive interference, and hence define the lateral boundaries of the beams produced by the superposition. The components $$\Delta k_x$$ and $$k_y$$ of one of the wave vectors are shown.

Applying the trigonometric identity for the sine of the sum of two angles (as we have done previously), equation (3.15) can be reduced to
 * $$ A = 2 \sin (k_y y - \omega t) \cos (\Delta k_x x) . $$ (3.16)

This is in the form of a sine wave moving in the $$y$$ direction with phase speed $$c_{phase} = \omega / k_y$$ and wavenumber $$k_y$$, modulated in the $$x$$ direction by a cosine function. The distance $$w$$ between regions of destructive interference in the $$x$$ direction tells us the width of the resulting beams, and is given by $$\Delta k_x w = \pi$$, so that
 * $$ w = \pi / \Delta k_x . $$ (3.17)

Thus, the smaller $$\Delta k_x$$, the greater is the beam diameter. This behavior is illustrated in figure 2.7.

Figure 2.8: Example of beams produced by two plane waves with the same wavelength moving in different directions. The wave vectors of the two waves are $$\mbox{k} = (\pm 0.1, 1.0)$$. Regions of positive displacement are illustrated by vertical hatching, while negative displacement has horizontal hatching.

Figure 2.8 shows an example of the beams produced by superposition of two plane waves of equal wavelength oriented as in figure 2.7. It is easy to show that the transverse width of the resulting wave packet satisfies equation (2.17).

Two Waves of Differing Wavelength
In the third example of figure 2.6, the frequency of the wave depends only on the direction of the wave vector, independent of its magnitude, which is just the reverse of the case for an isotropic dispersion relation. In this case different plane waves with the same frequency have wave vectors which point in the same direction, but have different lengths.

More generally, one might have waves for which the frequency depends on both the direction and magnitude of the wave vector. In this case, two different plane waves with the same frequency would typically have wave vectors which differed both in direction and magnitude.

Mathematically, we can represent the superposition of these two waves as a generalization of equation (2.15):
 * $$ A = \sin [ - \Delta k_x x + (k_y + \Delta k_y ) y - \omega t ] + \sin [ \Delta k_x x + (k_y - \Delta k_y ) y - \omega t ] . $$ (3.18)

In this equation we have given the first wave vector a $$y$$ component $$k_y + \Delta k_y$$ while the second wave vector has $$k_y - \Delta k_y$$. As a result, the first wave has overall wavenumber $$k_1 = [ \Delta k_x^2 + (k_y + \Delta k_y )^2 ]^{1/2}$$ while the second has $$k_2 = [ \Delta k_x^2 + (k_y - \Delta k_y )^2 ]^{1/2}$$, so that $$k_1 \ne k_2$$. Using the usual trigonometric identity, we write equation (2.18) as
 * $$ A = 2 \sin (k_y y - \omega t ) \cos ( - \Delta k_x x + \Delta k_y y ) . $$ (3.19)

To see what this equation implies, notice that constructive interference between the two waves occurs when $$- \Delta k_x x + \Delta k_y y = m \pi$$, where $$m$$ is an integer. Solving this equation for $$y$$ yields $$y = ( \Delta k_x / \Delta k_y )x + m \pi / \Delta k_y$$, which corresponds to lines with slope $$\Delta k_x / \Delta k_y$$. These lines turn out to be perpendicular to the vector difference between the two wave vectors, $$\mbox{k}_2 - \mbox{k}_1 = ( 2 \Delta k_x, -2 \Delta k_y )$$. The easiest way to show this is to note that this difference vector is oriented so that it has a slope $$- \Delta k_y / \Delta k_x$$. Comparison with the $$\Delta k_x / \Delta k_y$$ slope of the lines of constructive interference indicates that this is so.

Figure 2.10: Example of beams produced by two plane waves with wave vectors differing in both direction and magnitude. The wave vectors of the two waves are $$\mbox{k}_1 = ( -0.1, 1.0)$$ and $$\mbox{k}_2 = ( 0.1, 0.9)$$. Regions of positive displacement are illustrated by vertical hatching, while negative displacement has horizontal hatching.

An example of the production of beams by the superposition of two waves with different directions and wavelengths is shown in figure 2.10. Notice that the wavefronts are still horizontal, as in figure 2.8, but that the beams are not vertical, but slant to the right.

Figure 2.11: Illustration of factors entering the addition of two plane waves with the same frequency. The wave fronts are perpendicular to the vector average of the two wave vectors, $$\mbox{k}_0 = ( \mbox{k}_1 + \mbox{k}_2 )/2$$, while the lines of constructive interference, which define the beam orientation, are oriented perpendicular to the difference between these two vectors, $$\mbox{k}_2 - \mbox{k}_1$$.

Figure 2.11 summarizes what we have learned about adding plane waves with the same frequency. In general, the beam orientation and the lines of constructive interference are not perpendicular to the wave fronts. This only occurs when the wave frequency is independent of wave vector direction.

Many Waves with the Same Wavelength
As with wave packets in one dimension, we can add together more than two waves to produce an isolated wave packet. We will confine our attention here to the case of an isotropic dispersion relation in which all the wave vectors for a given frequency are of the same length.

Figure 2.12 shows an example of this in which wave vectors of the same wavelength but different directions are added together. Defining $$\alpha_i$$ as the angle of the $$i$$th wave vector clockwise from the vertical, as illustrated in figure 2.12, we could write the superposition of these waves at time $$t = 0$$ as $$A = \sum_i A_i \sin ( k_{xi} x + k_{yi} y )$$
 * $$= \sum_i A_i \sin [kx \sin ( \alpha_i ) + ky \cos ( \alpha_i ) ]$$ (3.20)

where we have assumed that $$k_{xi} = k \sin ( \alpha_i )$$ and $$k_{yi} = k \cos ( \alpha_i )$$. The parameter $$k = \vert \mbox{k} \vert$$ is the magnitude of the wave vector and is the same for all the waves. Let us also assume in this example that the amplitude of each wave component decreases with increasing $$\vert \alpha_i \vert$$:
 * $$ A_i = \exp [-( \alpha_i / \alpha_{max} )^2 ] . $$ (3.21)

The exponential function decreases rapidly as its argument becomes more negative, and for practical purposes, only wave vectors with $$\vert \alpha_i \vert \le \alpha_{max}$$ contribute significantly to the sum. We call $$\alpha_{max}$$ the spreading angle.

Figure 2.13: Plot of the displacement field $$A(x,y)$$ from equation (2.20) for $$\alpha _{max} = 0.8$$ and $$k = 1$$.

Figure 2.13 shows what $$A(x,y)$$ looks like when $$\alpha_{max} = 0.8 \mbox{ radians}$$ and $$k = 1$$. Notice that for $$y = 0$$ the wave amplitude is only large for a small region in the range $$-4 < x < 4$$. However, for $$y > 0$$ the wave spreads into a broad semicircular pattern.

Figure 2.14: Plot of the displacement field $$A(x,y)$$ from equation (2.20) for $$\alpha _{max} = 0.2$$ and $$k = 1$$.

Figure 2.14 shows the computed pattern of $$A(x,y)$$ when the spreading angle $$\alpha_{max} = 0.2 \mbox{ radians}$$. The wave amplitude is large for a much broader range of $$x$$ at $$y = 0$$ in this case, roughly $$-12 < x < 12$$. On the other hand, the subsequent spread of the wave is much smaller than in the case of figure 2.13.

We conclude that a superposition of plane waves with wave vectors spread narrowly about a central wave vector which points in the $$y$$ direction (as in figure 2.14) produces a beam which is initially broad in $$x$$ but for which the breadth increases only slightly with increasing $$y$$. However, a superposition of plane waves with wave vectors spread more broadly (as in figure 2.13) produces a beam which is initially narrow in $$x$$ but which rapidly increases in width as $$y$$ increases.

The relationship between the spreading angle $$\alpha_{max}$$ and the initial breadth of the beam is made more understandable by comparison with the results for the two-wave superposition discussed at the beginning of this section. As indicated by equation (2.17), large values of $$k_x$$, and hence $$\alpha $$, are associated with small wave packet dimensions in the $$x$$ direction and vice versa. The superposition of two waves doesn't capture the subsequent spread of the beam which occurs when many waves are superimposed, but it does lead to a rough quantitative relationship between $$\alpha_{max}$$ (which is just $$\tan^{-1} (k_x / k_y )$$ in the two wave case) and the initial breadth of the beam. If we invoke the small angle approximation for $$\alpha = \alpha_{max}$$ so that $$\alpha_{max} = \tan^{-1} (k_x / k_y ) \approx k_x / k_y \approx k_x / k$$, then $$k_x \approx k \alpha_{max}$$ and equation (2.17) can be written $$w = \pi / k_x \approx \pi / (k \alpha_{max} ) = \lambda / (2 \alpha_{max} )$$. Thus, we can find the approximate spreading angle from the wavelength of the wave $$\lambda $$ and the initial breadth of the beam $$w$$:
 * $$ \alpha_{max} \approx \lambda / (2d) \quad \mbox{(single slit spreading angle)} . $$ (3.22)

title: Waves/Plane Superposition


text:
Waves/Single slit Diffraction

Diffraction Through a Single Slit
Figure 2.15: Schematic behavior when a plane wave impinges on a narrow slit and a broad slit.

How does all of this apply to the passage of waves through a slit? Imagine a plane wave of wavelength $$\lambda $$ impingent on a barrier with a slit or opening of width $$w$$. The barrier transforms the plane wave with infinite extent in the lateral direction into a beam with initial transverse dimensions equal to the width of the slit. The subsequent development of the beam is illustrated in figures 2.13 and 2.14, and schematically in figure 2.15. In particular, if the slit width is comparable to the wavelength, the beam spreads broadly as in figure 2.13. If the slit width is large compared to the wavelength, the beam doesn't spread as much, as figure 2.14 illustrates. Equation (2.22) gives us an approximate quantitative result for the spreading angle if $$w$$ is interpreted as the width of the slit.

One use of the above equation is in determining the maximum angular resolution of optical instruments such as telescopes. The primary lens or mirror can be thought of as a rather large “slit”. Light from a distant point source is essentially in the form of a plane wave when it arrives at the telescope. However, the light passed by the telescope is no longer a plane wave, but is a beam with a tendency to spread. The spreading angle $$\alpha_{max}$$ is given by equation (2.22), and the telescope cannot resolve objects with an angular separation less than $$\alpha_{max}$$. Replacing $$w$$ with the diameter of the lens or mirror in equation (2.22) thus yields the telescope's angular resolution. For instance, a moderate sized telescope with aperture $$1 \mbox{ m}$$ observing red light with $$\lambda \approx 6 \times 10^{-7} \mbox{ m}$$ has a maximum angular resolution of about $$3 \times 10^{-7} \mbox{ radians}$$.

title: Waves/Single slit Diffraction


text:
Waves/Double slit Diffraction

Narrow Slits

Let us now imagine a plane sine wave normally impingent on a screen with two narrow slits spaced by a distance d, as shown in Figure 2.16. Since the slits are narrow relative to the wavelength of the wave impingent on them, the spreading angle of the beams is large and the diffraction pattern from each slit individually is a cylindrical wave spreading out in all directions, as illustrated in figure 2.13. The cylindrical waves from the two slits interfere, resulting in oscillations in wave intensity at the screen on the right side of figure 2.16.

Constructive interference occurs when the difference in the path lengths of the two rays is an integer multiple of the wavelength, λ:

 * $$l_2 - l_1 = m\lambda, \quad m = 0, \pm 1 , \pm 2 , \ldots \,$$

Similarly, destructive interference occurs at:

 * $$l_2 - l_1 = \left( m + \frac{1}{2} \right) \lambda, \quad m = 0, \pm 1 , \pm 2 , \ldots \,$$

If the distance from the slits to the screen, L is much greater than the slit separation, d, the rays l1 and l2 are approximately parallel and we can say that the path length difference is:

 * $$l_2 - l_1 = d \sin \theta\,$$

Substituting these two equations gives the following condition for constructive interference:

 * $$d \sin \theta = m\lambda, \quad m = 0, \pm 1 , \pm 2 , \ldots \,$$

The integer m is called the interference order and is the number of wavelengths by which the two paths differ. At every angle corresponding to integer m, constructive interference will be greatest and a "fringe" will be formed.

The distance from a point on the screen to the centre line, s, is related to θ as follows:
 * $$\tan \theta = \frac{s}{L}$$

When θ is small, we can say that:
 * $$\tan \theta \approx \sin \theta$$

We can therefore equate the expressions for position on the screen and fringe angles:
 * $$\frac{m \lambda}{d} \approx \frac{s}{L}$$

Rearranging gives an expression for the fringe spacing:
 * $$s \approx \frac{m \lambda L}{d} $$

The following conditions have to hold for this to be a good approximation:
 * The distance from the slits to the screen, L, must be much larger than the slit separation, d.
 * The angle, θ, to the fringe from the slits must be small.
 * The slits must be narrow compared to the wavelength, λ.

Example
Let us consider a setup with the following parameters:
 * d = 0.1 mm
 * λ = 2500 nm (infrared)

We expect to see a fringe spacing at 10m of:
 * $$s=\frac{\lambda L}{d}=\frac{2500 \times 10^{-9} \times 10}{0.1 \times 10^{-3}}=0.25m$$

First, let's look at a "snapshot" of the wave at a certain instance in time. The amplitude at a point, (x,y), is given by:
 * $$u(x,y,t)=

a\sin \left( k \sqrt{ \left( x-\frac{d}{2} \right)^2 + y^2} \right)+ a\sin \left( k \sqrt{ \left( x+\frac{d}{2} \right)^2 + y^2} \right) $$ where k is the wavenumber, given by 2π/λ. In this exercise, we will neglect the decreasing amplitude with distance, so the fringes stay bright over all space. The plot below shows a plot of this function. You can clearly see the circular propagation of each source, but an overall fringe structure is difficult to make out.

Now, the human eye and all light-measuring equipment do not detect the individual oscillations of a light wave, they measure intensity. Here, intensity is a function of the phase difference between the two sources, which in turn is directly related to the path length difference.
 * $$\delta = \frac{2\pi}{\lambda}\Delta l$$
 * $$I \approx 4 a^2 \cos^2 \frac{\delta}{2}$$

The plot below shows this intensity function. We see that a very clear fringe structure is revealed:

At this scale, the fringe structure is not clearly radial, it "bends" around the source. However, we can see that if we were to zoom out, the frenges diverge, and the ones near the centre, which are closest to perfectly radial, will be the ones that matter: In this plot, we see the predicted bright fringes at x=0mm, x=±250mm and x=±500mm.

title: Waves/Double slit Diffraction


text:
Waves/Diffraction Grating

Diffraction Gratings
Since the angular spacing $$\Delta \theta$$ of interference peaks in the two slit case depends on the wavelength of the incident wave, the two slit system can be used as a crude device to distinguish between the wavelengths of different components of a non-sinusoidal wave impingent on the slits. However, if more slits are added, maintaining a uniform spacing $$d$$ between slits, we obtain a more sophisticated device for distinguishing beam components. This is called a diffraction grating.

Figures 2.17-2.19 show the amplitude and intensity of the diffraction pattern for gratings with 2, 4, and 16 slits respectively. Notice how the interference peaks remain in the same place but increase in sharpness as the number of slits increases.

The width of the peaks is actually related to the overall width of the grating, $$w = nd$$, where $$n$$ is the number of slits. Thinking of this width as the dimension of large single slit, the single slit equation, $$\alpha_{max} = \lambda /(2w)$$, tells us the angular width of the peaks.

Whereas the angular width of the interference peaks is governed by the single slit equation, their angular positions are governed by the two slit equation. Let us assume for simplicity that $$\vert \theta \vert << 1$$ so that we can make the small angle approximation to the two slit equation, $$m \lambda = d \sin \theta \approx d \theta$$, and ask the following question: How different do two wavelengths have to be in order that the interference peaks from the two waves not overlap? In order for the peaks to be distinguishable, they should be separated in $$\theta $$ by an angle $$\Delta \theta = m \Delta \lambda /d$$, which is greater than the angular width of each peak, $$\alpha_{max}$$:
 * $$ \Delta \theta > \alpha_{max} . $$ (3.24)

Substituting in the above expressions for $$\Delta \theta$$ and $$\alpha_{max}$$ and solving for $$\Delta \lambda$$, we get $$\Delta \lambda > \lambda /(2mn)$$, where $$n = w/d$$ is the number of slits in the diffraction grating. Thus, the fractional difference between wavelengths which can be distinguished by a diffraction grating depends solely on the interference order $$m$$ and the number of slits $$n$$ in the grating:
 * $$ \frac{\Delta \lambda}{\lambda} > \frac{1}{2mn} . $$ (3.25)

More information about diffraction and diffractive optics

title: Waves/Diffraction Grating