A Ton of Crap (109 page)

GROUP THEORY

Abstract Groups
So far, all of the types of groups have been concrete. They have used either numbers, matrices, or permutations. In the late nineteenth century, the idea of abstract groups was created. Abstract groups have abstract properties and are presented with generators and relations. An abstract group can be represented as:

G = < S | R >

An example of an abstract group would be the Cyclic Group, a group that is generated from one single element.

GAS LAWS

Avogadro’s Law
In 1811, Italian chemist Amedeo Avogadro hypothesized that two gases with the same pressure, volume, and temperature would also contain the same number of molecules, regardless of any physical or chemical properties. Avogadro’s law can be written as:

V
represents the volume,
n
represents the number of moles (or substance) in the gas, and
k
is a constant.

From Avogadro’s law, it was determined that the ideal gas constant (
k
) is the same value for any gas, which means:

PASHTO

Writing System
The Pashto alphabet, which has 45 letters, is derived from the Arabic alphabet, but features letters that represent sounds not found in Arabic. All of the 28 letters from the Arabic system are used, and there are three letters in common with the Persian and Urdu alphabets. In total, there are 45 letters to the Pashto alphabet. In the late eighteenth century, the spelling system was standardized.

THE CULTURAL REVOLUTION IN CHINA

End of the Cultural Revolution
By 1968, the Chinese economy was close to collapsing and the factionalism in the Red Guard was creating havoc. In 1971, the chaos of the Cultural Revolution had died down with the People’s Liberation Army. From 1972 to 1976, with both Chairman Mao and the premier in deteriorating health, there was a great struggle over whether to continue the Cultural Revolution in the succession phase. Mao’s propagandists blamed the chaos of the Cultural Revolution on four people, known as the “Gang of Four” (one of whom was Mao Zedong’s wife). In October of 1976, the Gang of Four were arrested, thus ending the Cultural Revolution. Mao Zedong died on September 9, 1976.

VICTORIAN LITERATURE

Late Victorian Period
The Victorian era can be divided into two parts: the early Victorian period (which ended around 1870), and the late Victorian period (which lasted from 1890 to 1918). In the late Victorian period, the principles that followed throughout the Victorian era were rejected. There was a return to fantasy, with such works as Robert Lewis Stevenson’s
The Strange Case of Dr. Jekyll and Mr. Hyde
, and the emergence of the “problem novel.” Problem novels focused on the institution of marriage and the role of the sexes and sexual identity.

GROUP THEORY

Rubik’s Cube
Group theory sounds incredibly complicated. To understand how group theory works, think of the Rubik’s Cube. The Rubik’s Cube can be thought of as a mathematical group because it meets all four requirements of being a group, and permutations are each of the elements of the group. In order to solve the Rubik’s Cube, you need to perform certain actions in a particular order.

GAS LAWS

Graham’s Law
Graham’s law deals with effusion, the process where molecules escape from a container through a hole and do not collide. Graham’s law states that the rate of effusion is inversely proportional to the square root of the molecular masses. Graham’s law can be written as:

Rate
₁
and Rate
₂
are the rates of effusion for the first and second gases, respectively, and
M
₁
and
M
₂
are the molar masses of the first and second gases, respectively.

PASHTO