White people felt ignored because Spaniards were sent by their governor, and resented wealthy mixed heritage people who could “buy” whiteness. The creoles started calling themselves Americans and not Spaniards to demonstrate that they wanted independence. In 1808, Napoleon conquered Spain, and made his brother, Joseph Bonaparte the new king. The colonies in Latin America rebelled because they said they were loyal to the old king, Charles IV of Spain and not Napoleon.
On September 6th 1815 Simón Bolívar wrote a letter from Jamaica. He explained the causes and reasons why all of South America or parts of it should be independent (free from Spain's ruling). Simón Bolívar was tired of how Venezuela and other countries were treated like slaves and how they were not free. He said “We have been harassed by a conduct which has not only deprived us of our rights but has kept us in a sort of permanent infancy with regard to public affairs.” He kept saying in the Jamaica letter why it's important to be free. “We are still in a position lower than slavery, and therefore it is more difficult for us to rise to the enjoyment of freedom.” This means they could not even enjoy freedom. "Because successes have been partial and spasmodic, we must not lose faith. We are young in the ways of almost all the arts and sciences, although, in a certain manner, we are old in the ways of civilized society."
On May 26, 1819 Bolívar gathered with a group of guerrillas that wanted to defeat the Spanish army. They got supplies and they crossed hundreds of miles of plains, swamps, rivers, etc. Many of the men died of hunger, diseases, and other causes on the way there. Crossing plains on August 7, they encountered the royalists and won the battle in Boyacá on August 10. Bolívar then occupied Boyacá, Colombia. Bolívar won the fight of Carabobo in June 1821, and then another in Caracas. A few days later and Venezuela was free of the Spanish royalists, then Bolívar went South and conquered Quito. On July 27, 1822 Simón Bolívar and José de San Martín met in the Guayaquil Conference. They were preparing to march across the Andes to Peru to defeat the Spanish royalists in August of 1824. San Martin resigned his powers in Peru and went back to Argentina. Later he went to Europe. Bolívar launched his campaign and soon he won a small but important battle at Junín. The royalists retreated and eventually lost.
Bolívar said that his people were in a position "lower than slavery", but many of them owned slaves themselves. Alexandre Pétion, the president of Haiti, said that he would help Bolívar fight if he abolished slavery as part of independence. Bolívar agreed, but only because he was afraid the slaves would revolt against the slaveowners, like they did in Haiti, and he only freed slaves who agreed to fight in his army. Even though Pétion helped him, Bolívar never freed all the slaves, and slavery was not abolished until the 1850s in Colombia, Venezuela, and Ecuador.
He is still remembered and celebrated for helping many of the Latin American countries achieve independence. People called him "El Liberator" because of this. Some people hated him because they thought he was a traitor, and he was going to be a dictator.
Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a statement about the sides of a right triangle.
One of the angles of a right triangle is always equal to 90 degrees. This angle is the right angle. The two sides next to the right angle are called the legs and the other side is called the hypotenuse. The hypotenuse is the side opposite to the right angle, and it is always the longest side. It was discovered by Vasudha Arora.
The Pythagorean theorem says that the area of a square on the hypotenuse is equal to the sum of the areas of the squares on the legs. In this picture, the area of the blue square added to the area of the red square makes the area of the purple square. It was named after the Greek mathematician Pythagoras:
If the lengths of the legs are "a" and "b", and the length of the hypotenuse is "c", then, formula_1.
There are many different proofs of this theorem. They fall into four categories:
One proof of the Pythagorean theorem was found by a Greek mathematician, Eudoxus of Cnidus.
The proof uses three lemmas:
The proof is:
We can get another proof of the Pythagorean theorem by using similar triangles.
From the image, we know that formula_4. And by replacing equations (1) and (2):
Multiplying by c:
Pythagorean triples or triplets are three whole numbers which fit the equation formula_1.
The triangle with sides of 3, 4, and 5 is a well known example. If a=3 and b=4, then formula_8 because formula_9. This can also be shown as formula_10
The three-four-five triangle works for all multiples of 3, 4, and 5. In other words, numbers such as 6, 8, 10 or 30, 40 and 50 are also Pythagorean triples. Another example of a triple is the 12-5-13 triangle, because formula_11.
A Pythagorean triple that is not a multiple of other triples is called a primitive Pythagorean triple. Any primitive Pythagorean triple can be found using the expression formula_12, but the following conditions must be satisfied. They place restrictions on the values of formula_13 and formula_14.
If all four conditions are satisfied, then the values of formula_13 and formula_14 create a primitive Pythagorean triple.
formula_30 and formula_31 create a primitive Pythagorean triple. The values satisfy all four conditions. formula_32, formula_33 and formula_34, so the triple formula_35 is created.
Temperature
Temperature is how hot or cold something is. Our bodies can feel the difference between something which is hot and something which is cold. To measure temperature more accurately, a thermometer can be used. Thermometers use a temperature scale to record how hot or cold something is. The scale used in most of the world is in degrees Celsius, sometimes called "centigrade". In the USA and some other countries and locations, degrees Fahrenheit are more often used while scientists mostly use kelvins to measure temperature because it never goes below zero.
Scientifically, temperature is a physical quantity which describes how quickly molecules are moving inside a material. In solids and liquids the molecules are vibrating around a fixed point in the substance, but in gases they are in free flight and bouncing off each other as they travel. In a gas the temperature, pressure and volume of the gas are closely related by a law of physics.
When they invented temperature scales scientists found there were certain things which were always around the same temperature:
Temperature is not the same as heat. Heat is energy which moves from one thing, cooling it, to another, heating it. Temperature is a measure of the movements (vibration) of the molecules inside a thing. If the thing has a high temperature, it means the average speed of its molecules is fast. A thing may have a high temperature but because it contains very few or light atoms it has very little heat.
The amount of heat that is needed to make a substance one degree higher is called its heat capacity. Different substances have different heat capacities. For example, a kilogram of water has more heat capacity than a kilogram of steel. This means that more energy is needed to make the temperature of water 1°C hotter than is needed to make the temperature of steel 1°C hotter.
Temperature is also important in weather and climate. It is related to the amount of heat energy in the air. Isotherm maps are used to show how temperature is different across an area. Temperature will be different during different times of day, different seasons and in different places. It is affected by how much heat reaches the place from the suns rays (insolation), how high the place is above the level of the sea, and how much heat is brought to the place by the movement of winds and ocean currents.
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