π can also be calculated by only using mathematical methods. Most methods used for calculating the value of π have desirable mathematical properties. However, they are hard to understand without knowing trigonometry and calculus. However, some methods are quite simple, such as this form of the Gregory-Leibniz series:
While that series is easy to write and calculate, it is not easy to see why it equals π. A much easier way to approach is to draw an imaginary circle of radius r centered at the origin. Then any point ("x","y") whose distance d from the origin is less than r, calculated by the Pythagorean theorem, will be inside the circle:
Finding a set of points inside the circle allows the circle's area A to be estimated, for example, by using integer coordinates for a big r. Since the area A of a circle is π times the radius squared, π can be approximated by using the following formula:
Capitalization
Capitalise (British spelling) or capitalize (North American spelling) means to make one or more letters upper case. The first letter of a sentence is capitalised in many languages, as are the first letters of proper nouns such as names of people and places. In German, however, all nouns are capitalized. It is the only language to do that.
In the Latin alphabet, which is used in English, these are the upper case or capital letters:
A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z
These are the lower case letters:
a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z
The homonym capitalize is a different word, and means "to fully fund as an investment".
Cuba
Cuba is an island country in the Caribbean Sea. The country is made up of the big island of Cuba, the Isla de la Juventud island ("Isle of Youth"), and many smaller islands. Havana is the capital of Cuba. It is the largest city. The second largest city is Santiago de Cuba. In Spanish, the capital is called "La Habana". Cuba is near the United States, Mexico, Haiti, Jamaica and the Bahamas. People from Cuba are called Cubans ("cubanos" in Spanish). The official language is Spanish. Cuba is warm all year.
In 1492, Christopher Columbus landed on the island of Cuba. He claimed it for the Kingdom of Spain. Cuba became a Spanish colony until the Spanish–American War of 1898. After the war, it was part of the United States. It gained independence in 1902.
In 1959, guerrilla fighters led by Fidel Castro and Che Guevara overthrew Cuba's dictator, Fulgencio Batista, in what became the Cuban Revolution. Castro began making relations with the Soviet Union and tried to close a lot of American businesses in Cuba; the United States did not like this. In 1961 Castro officially announced that his government was socialist. The US attempted to invade Cuba to regain control of it and overthrow it's communist led government but failed. The Communist Party of Cuba was created in 1965 and has ruled the island ever since. Today, Cuba is the only communist state outside of Asia, in the Caribbean, and in the western hemisphere.
Cuba is famous for many types of music, especially dance music such as the Salsa and Mambo. Because Cubans have ancestors from Spain, Africa, South America and North America, Cuban music is special and different.
Reading is very popular in Cuba. Many people especially enjoy reading books or things that come from outside the country, even though the government does not approve of this. They also love music and sports. Cuban music is very lively. This is because a lot of it comes from African and Spanish rhythms. Baseball, basketball, and athletics events are loved by many Cuban people. The Cheifs football-team took at one Football-World-Cup part. In 1938, they reached the quarter-final and lost against Sweden 0:8.
Before Cuba was conquered by the Spaniards, three tribes lived on the island. They were the Taínos, the Ciboneys, and the Guanajatabeyes. The Taínos were the largest and most common of the three tribes. They farmed crops such as beans, corn, squash, and yams. The Taínos also slept in hammocks which the Spaniards would introduce to the rest of the world. Then, in 1492, Christopher Columbus arrived in Cuba on his first trip to the Americas. Three years later he claimed the islands for the Spanish. The Spanish began to rule Cuba afterwards. The Spanish brought thousands of slaves from Africa to Cuba to work for them. Most of the native Cubans died because of the new diseases brought by the Spanish and Africans. The Spanish also treated the native Cubans very cruelly and massacred many of them.
The Spanish ruled for many years. Cuba became the most important producer of sugar. In the early 1800s, Cubans rebelled against the Spanish rulers, but failed until 1898, when the United States went to war with the Spanish and defeated them. Cuba became American for four years afterwards, before it became an independent republic in 1902. Even though Cuba was independent, the Americans still controlled the island by a law called the Platt Amendment. In 1933 the Cubans stopped the Platt Amendment, but the Americans still had a big say in Cuban politics. Americans owned most of Cuba’s businesses. The Americans supported the leader Fulgencio Batista, who was seen by many Cubans as corrupt.
In addition to political control, the United States also exercised significant control over the Cuban economy. At the time, Cuba was a monoculture economy. While they produced coffee, tobacco, and rice, they relied primarily on sugar. Thus, they were known by other countries as the "sugar bowl of the world." The United States bought sugar from the Republic of Cuba at a price higher than the global standard. In exchange, Cuba was to give preference to the United States, and its industries. Cuba depended on the United States and their investments. Cuba was not industrialized and needed the revenue for goods and oil. They also needed the US investment for gas, electricity, communications, railways, and banks. While Cuban workers had better conditions than other countries in the continent, they still faced inequality, lack of infrastructure, high illiteracy rates, and a lack of full-time work (the sugar industry was seasonal).
In 1959, Fidel Castro led a revolution against Fulgencio Batista. Castro took power in Cuba with Che Guevara from Argentina, his brother Raul, and others who fought against Batista. Castro made many changes to Cuba. He ended American ownership of Cuban businesses. This made Castro unpopular in America and the United States banned all contact with Cuba. Many Cubans went to America because of this. In 1961, the Americans helped some of these Cubans to attack Cuba and try to remove Castro, but they failed. Castro then asked the Soviet Union to help defend them from the Americans, which they did. The Soviet Union put nuclear weapons in Cuba and aimed them at the United States. American President Kennedy demanded that they be removed or a new war would begin. This was known as the "Cuban Missile Crisis". The Soviet Union removed the missiles when the United States agreed to not continue attacking Cuba and to remove missiles from Turkey.
Cuba became a communist-led country like the Soviet Union after this. The Soviet Union bought most of Cuba’s sugar for expensive prices. Cuba spent this money on health, education and the army. This made Cuba’s schools and hospitals some of the best in the world. The army fought in Africa to support black Africans against the white South African army. Cuba also supported groups in South America fighting against the dictators of those countries.