Thus, teahouses were established along the roadside. An imperial physician in the third century wrote that combining tea with food would lead to excessive weight gain.

People later discovered that tea can aid in digestion, so teahouse owners began adding various snacks. The unique culinary art dim sum originated with the Cantonese in Guangzhou or Canton , who over the centuries transformed yum cha from a relaxing respite to a loud and happy dining experience.

In Hong Kong , and in most cities and towns in Guangdong province, many restaurants start serving dim sum as early as five in the morning.

It is a tradition for the elderly to gather to eat dim sum after morning exercises. For many in southern China, yum cha is treated as a weekend family day.

More traditional dim sum restaurants typically serve dim sum until mid-afternoon. However, in modern society, it has become commonplace for restaurants to serve dim sum at dinner time; various dim sum items are even sold as take-out for students and office workers on the go.

A traditional dim sum brunch includes various types of steamed buns such as cha siu bao a steamed bun filled with barbecue pork , rice or wheat dumplings and rice noodle rolls , which contain a range of ingredients , including beef , chicken, pork, prawns , and vegetarian options.

Many dim sum restaurants also offer plates of steamed green vegetables, roasted meats, congee and other soups. Dessert dim sum is also available and many places offer the customary egg tart.

Dim sum is usually eaten as breakfast or brunch. Dim sum can be cooked by steaming and frying , among other methods. The serving sizes are usually small and normally served as three or four pieces in one dish.

It is customary to order family style, sharing dishes among all members of the dining party. Because of the small portions, people can try a wide variety of food.

Dim sum brunch restaurants have a wide variety of dishes, usually several dozen. Among the standard fare of dim sum are the following:.

The drinking of tea is as important to dim sum as the food. The type of tea to serve on the table is typically one of the first things the server asks dining customers.

Several types of tea are served during dim sum:. Chrysanthemum tea — Chrysanthemum tea does not actually contain any tea leaves.

Instead it is a flower-based tisane made from chrysanthemum flowers of the species Chrysanthemum morifolium or Chrysanthemum indicum , which are most popular in East Asia.

However, Chrysanthemum flowers are often paired with Pu-erh tea, and this is often referred to as guk pou Chinese: Green tea — Freshly picked leaves only go through heating and drying processes, but do not undergo oxidation.

This enables the leaves to keep their original green color and retain most natural substances like polyphenols and chlorophyll contained within the leaves.

This kind of tea is produced all over China and is the most popular category of tea. Representative varieties include Dragon Well Chinese: Oolong tea — The tea leaves are partially oxidized, imparting to them the characteristics of both green and black teas.

Its taste is more similar to green tea than black tea, but has a less "grassy" flavor than green tea. The three major oolong-tea producing areas are on the southeast coast of China e.

Fujian, Guangdong and Taiwan. It is originally cultivated in Fujian province and is a premium variety of Oolong tea with delightful fragrance.

Pounei tea Cantonese or Pu-erh tea Mandarin — The tea has undergone years of fermentation, giving them a unique earthy flavor. This variety of tea is usually compressed into different shapes like bricks, discs and bowls.

Scented teas — There can be various mixtures of flowers with green tea, black tea or oolong tea. Flowers used include jasmine, gardenia, magnolia, grapefruit flower, sweet-scented osmanthus and rose.

There are strict rules about the proportion of flowers to tea. Jasmine tea is the most popular type of scented tea, and is often the most popular type of tea served at yum cha establishments.

The above teas are produced in most of China. Chinese tea bushes Camellia sinensis are cultivated in the mountain areas of tropical and subtropical regions or wherever there is a proper climate, sufficient humidity, adequate sunshine and fertile soil.

Chinese tea is classified in many ways, e. The main processing methods include oxidation, fermentation, heating, drying and addition of other ingredients like flowers, herbs or fruits.

These help to develop the special flavor of the raw tea leaves. One aspect unique to dim sum is its method of serving in specialized dim sum brunch restaurants or teahouses.

For example, a basket of dumplings may be considered a small dish, while a bowl of congee or plate of lo mai gai may be considered a large dish.

Dishes are then priced accordingly by size, with orders typically recorded with a rubber stamp onto a bill card that remains on the table.

Servers in some restaurants use distinctive stamps, so that sales statistics for each server can be recorded. Menu items not typically considered dim sum fare, such as a plate of chow mein , are often available; they are typically branded as " kitchen " dishes on menus and are individually priced.

When done eating, the customers simply call the waiters over and the bill is calculated based on the number of stamps in each priced section. As a means of attracting customers at less busy times, many restaurants have promotional periods on certain days, usually in the early morning or late afternoon.

This typically involves charging a fixed price for certain dishes. Typically, the "small", "medium" and "large" items are all charged at the usual price for "small" items; the rule would not apply to "extra large", "special", or "kitchen" dishes.

In some places the "tea fee" may also be waived, or a discount be placed on the entire order. Where such periods exist the bill card would have a designated section that allows the items that were ordered during the period and to be easily recognized and charged appropriately.

This is defined as:. Informal writing sometimes omits the definition of the index and bounds of summation when these are clear from context, as in:.

One often sees generalizations of this notation in which an arbitrary logical condition is supplied, and the sum is intended to be taken over all values satisfying the condition.

Here are some common examples:. A similar notation is applied when it comes to denoting the product of a sequence, which is similar to its summation, but which uses the multiplication operation instead of addition and gives 1 for an empty sequence instead of 0.

These degenerate cases are usually only used when the summation notation gives a degenerate result in a special case. In the notation of measure and integration theory, a sum can be expressed as a definite integral ,.

Given a function f that is defined over the integers in the interval [ m , n ] , one has. This is the analogue in calculus of finite differences of the fundamental theorem of calculus , which states.

Using binomial theorem , this may be rewritten. Many such approximations can be obtained by the following connection between sums and integrals , which holds for any:.

For more general approximations, see the Euler—Maclaurin formula. For summations in which the summand is given or can be interpolated by an integrable function of the index, the summation can be interpreted as a Riemann sum occurring in the definition of the corresponding definite integral.

One can therefore expect that for instance. However, for a given summation n is fixed, and little can be said about the error in the above approximation without additional assumptions about f: The formulae below involve finite sums; for infinite summations or finite summations of expressions involving trigonometric functions or other transcendental functions , see list of mathematical series.

In the following summations, a is supposed to be different of 1. There exist very many summation identities involving binomial coefficients a whole chapter of Concrete Mathematics is devoted to just the basic techniques.

Some of the most basic ones are the following. The following are useful approximations using theta notation:. From Wikipedia, the free encyclopedia.

This article is about sums of several elements. For more elementary aspects, see Addition. For infinite sums, see Series mathematics.

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