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Authors: Paul Kleinman

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The First Voyage
Columbus prepared three ships, the
Nina
, the
Pinta
, and the
Santa Maria
, for their journey. Columbus was the captain of the
Santa Maria
and his brothers were the captains of the other ships. On August 3, 1492, they set sail. On October 12, they landed on what is now the island of San Salvador in the Bahamas and took possession of the island. Columbus soon found Cuba (which he believed to be China), and in December, he reached Hispaniola (which Columbus believed to be Japan), and established a colony of thirty-nine men. In March of 1493, Columbus returned to Spain with riches, spices, and “Indian” captives.

DIALECTS

Standard Dialects
A standard dialect, also known as a standard language, is a dialect that begins to be used in other ways, rather than just by the small group of people who speak it. Standard dialects appear in literature and administrative work, for example, and also have support from institutions. Standard English, Standard Australian English, and Standard Canadian English are all dialects of the English language.

PYTHAGOREAN THEOREM

Proof with Triangles That Are Similar
The simplest way to prove the Pythagorean theorem is by using similar triangles. In similar triangles, corresponding parts are proportional, regardless of how big or small the two triangles are. This type of proof depends on length and not on area. The equation for this proof is:

and

From there,
a
2 =
c
 × 
e
and
b
2 = 
c
 × 
d

If you add them together, you get

a
2 + 
b
2 = 
c
 × 
e
 + 
c
 × 
d

which leads to

a
2 + 
b
2 = 
c
2

THE BIG BANG

The Universe Expands
Once the singularity formed, it began to expand and inflate (the big bang). The big bang was not an expansion of matter in space, but rather the creation and expansion of the space that carried matter. The big bang started at extremely hot temperatures, and as it expanded it began cooling. The universe is still expanding and cooling even to this day.

SWEDISH

Old Swedish
Old Swedish was the language spoken in 1225, and it lasted until the late fourteenth century. The language was much more complex than what is spoken today, and the influence from Middle Low German was very clear. The Christian Church played an important role in society, and documents were written in Latin script. Words from Latin, Greek, and Dutch were all incorporated into Old Swedish.

LESSON 13C
COLUMBUS AND THE NEW WORLD

The Second Voyage
In October of 1493, Columbus set sail with a fleet of seventeen ships and 1,500 colonists. In November, they landed in the Lesser Antilles and discovered Puerto Rico and the Leeward Islands. Upon returning to Hispaniola, Columbus found that the original colony had been killed by the natives. Columbus established another colony and then set sail once again, exploring Cuba and finding Jamaica. As Columbus left for Spain, his brother stayed in Hispaniola and founded Santo Domingo, which was the first permanent European settlement of the Americas.

DIALECTS

Social Dialects
Difference in dialects is directly related to social status. Those that are highly educated tend to belong to a higher social class and use the standard dialect, whereas the lower classes, which tend to be less educated, preserve the original dialect of the region. In urban areas, innovations in the dialect tend to be made, whereas the dialect spoken in rural areas is more of the traditional geographic dialect.

Pythagorean Theorem

Euclid’s Proof
In Euclid’s proof, a large square is divided into two rectangles, one large, one small. Of the larger rectangle, a triangle is created that is half of the area of the rectangle. The same thing is done with the smaller rectangle, so you have two congruent triangles.

After working through a set of rules, you will end up with AB2 + AC2 = BC2

THE BIG BANG
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